Matrices and Determinants · Mathematics · MHT CET

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MCQ (Single Correct Answer)

1

If $\left[\begin{array}{lll}1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}12 \\ 15 \\ 13\end{array}\right]$, then the value of $x^2+y^2+z^2=$

MHT CET 2025 20th April Evening Shift
2

If $A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$, then $A^T A^{-1}=$

MHT CET 2025 20th April Morning Shift
3

If $A=\left[\begin{array}{rr}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha I+\beta A \alpha, \beta \in R$ where I is the identity matrix of order 2 , then $4(\alpha+\beta)=$

MHT CET 2025 19th April Evening Shift
4
If $A=\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, where $A_{21}, A_{22}, A_{23}$ are cofactors of $a_{21}, a_{22}, a_{23}$ respectively, then the value of $\mathrm{a}_{21} \mathrm{~A}_{21}+\mathrm{a}_{22} \mathrm{~A}_{22}+\mathrm{a}_{23} \mathrm{~A}_{23}=$
MHT CET 2025 19th April Morning Shift
5

Let $A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]$ and $A^{-1}=\alpha \mathrm{I}+\beta \mathrm{A}, \alpha, \beta \in \mathbb{R}$, I is the identity matrix of order 2 , then $4(\alpha-\beta)$ is

MHT CET 2024 16th May Evening Shift
6

If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$, $\bar{c}=c_1 \hat{i}+c_2 \hat{j}+c_3 \hat{k}$ and $\left[\begin{array}{lll}3 \bar{a}+\bar{b} & 3 \bar{b}+\bar{c} & 3 \bar{c}+\bar{a}\end{array}\right]=\lambda\left|\begin{array}{lll}\overline{\mathrm{a}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{a}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{a}} \cdot \hat{\mathrm{k}} \\ \overline{\mathrm{b}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{b}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{b}} \cdot \hat{\mathrm{k}} \\ \overline{\mathrm{c}} \cdot \hat{\mathrm{i}} & \overline{\mathrm{c}} \cdot \hat{\mathrm{j}} & \overline{\mathrm{c}} \cdot \hat{\mathrm{k}}\end{array}\right|,$ then the value of $\lambda$ is

MHT CET 2024 16th May Evening Shift
7

Let $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in \mathbb{R}^{+}$and $A^4=\left[a_{i j}\right]_2$. If $a_{11}=109$, then $\left(A^4\right)^{-1}=$

MHT CET 2024 16th May Morning Shift
8

If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ is equal to

MHT CET 2024 15th May Evening Shift
9

Let A and B be $3 \times 3$ real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations $\left(A^2 B^2-B^2 A^2\right) X=O$. where $X$ is $3 \times 1$ column matrix of unknown variables and $O$ is a $3 \times 1$ null matrix, has

MHT CET 2024 15th May Morning Shift
10

If $A\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ then $\left(A^2-5 A\right)^{-1}$ is

MHT CET 2024 11th May Evening Shift
11

Let $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$ such that $\mathrm{AX}=\mathrm{B}$, then $\mathrm{X}=$

MHT CET 2024 11th May Morning Shift
12

If $\mathrm{w}=\frac{-1-\mathrm{i} \sqrt{3}}{2}$ where $\mathrm{i}=\sqrt{-1}$, then the value of $\left|\begin{array}{ccc}1 & w & w^2 \\ w & w^2 & 1 \\ w^2 & 1 & w\end{array}\right|$ is

MHT CET 2024 10th May Evening Shift
13

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

MHT CET 2024 10th May Evening Shift
14

If $A+B=\left[\begin{array}{cc}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]$ where $A$ is symmetric and $B$ is skew-symmetric matrix, then the matrix $\left(A^{-1} B+A B^{-1}\right)$ at $\theta=\frac{\pi}{6}$ is given by

MHT CET 2024 10th May Morning Shift
15

For the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$, the matrix of cofactors is

MHT CET 2024 9th May Evening Shift
16

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & a & 3 \\ 3 & 2 & 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2 & 0 & b \\ 7 & -1 & -2 \\ c & 1 & 1\end{array}\right]$ and if matrix $B$ is the inverse of matrix $A$, then value of $4 a+2 b-c$ is

MHT CET 2024 9th May Morning Shift
17

Let $\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$ and $\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}_2$, (where $\mathrm{I}_2$ is unit matrix of order 2), then

MHT CET 2024 4th May Evening Shift
18

Suppose A is any $3 \times 3$ non-singular matrix and $(\mathrm{A}-3 \mathrm{I})(\mathrm{A}-5 \mathrm{I})=0$ where $\mathrm{I}=\mathrm{I}_3$ and $\mathrm{O}=\mathrm{O}_3$. Here $\mathrm{O}_3$ represent zero matrix of order 3 and $\mathrm{I}_3$ is an identity matrix of order 3 . If $\alpha A+\beta A^{-1}=4 I$, then $\alpha+\beta$ is equal to

MHT CET 2024 4th May Morning Shift
19

For the system $x-y+z=4,2 x+y-3 z=0$, $x+y+z=2$, the values of $x, y, z$ respectively are given by

MHT CET 2024 3rd May Evening Shift
20

If $A=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $A^{-1}=$

MHT CET 2024 3rd May Morning Shift
21

Let $X=\left[\begin{array}{l}\mathrm{a} \\ \mathrm{b} \\ \mathrm{c}\end{array}\right], \mathrm{A}=\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 0 & 1 \\ 3 & 2 & 1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{l}3 \\ 1 \\ 4\end{array}\right]$. If $A X=B$, then the value of $2 a-3 b+4 c$ will be

MHT CET 2024 2nd May Evening Shift
22

If $A=\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$, then $A^{-1}$ is

MHT CET 2024 2nd May Morning Shift
23

If $$A=\left[\begin{array}{ll}1 & -1 \\ 2 & -1\end{array}\right], B=\left[\begin{array}{cc}1 & 1 \\ 4 & -1\end{array}\right]$$, then $$(A+B)^{-1}$$ is

MHT CET 2023 14th May Evening Shift
24

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 0 & 2\end{array}\right].$$ If $$B=I-{ }^3 C_1(\operatorname{adj} A)+{ }^3 C_2(\operatorname{adj} A)^2-{ }^3 C_3(\operatorname{adj} A)^3$$, then the sum of all elements of the matrix B is

MHT CET 2023 14th May Morning Shift
25

If $$A=\left[\begin{array}{cc}1 & \tan x \\ -\tan x & 1\end{array}\right]$$, then $$A^T \cdot A^{-1}=$$

MHT CET 2023 13th May Evening Shift
26

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$ and $$A_{i j}$$ is a cofactor of $$a_{i j}$$ then the value of $$a_{21} A_{21}+a_{22} A_{22}+a_{23} A_{23}$$ is

MHT CET 2023 13th May Morning Shift
27

If $$A=\left[\begin{array}{cc}2 a & -3 b \\ 3 & 2\end{array}\right]$$ and $$A \cdot \operatorname{adj} A=A A^T$$, then $$2 a+3 b$$ is

MHT CET 2023 12th May Evening Shift
28

If the matrix $$\mathrm{A}=\left[\begin{array}{cc}1 & 2 \\ -5 & 1\end{array}\right]$$ and $$\mathrm{A}^{-1}=x \mathrm{~A}+y \mathrm{I}$$, when $$I$$ is a unit matrix of order 2 , then the value of $$2 x+3 y$$ is

MHT CET 2023 12th May Morning Shift
29

If $$\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]$$ where $$\mathrm{i}=\sqrt{-1}$$ and $$\mathrm{B}=\mathrm{A}^{2029}$$, then $$\mathrm{B}^{-1}=$$

MHT CET 2023 11th May Evening Shift
30

If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$|A|=4$$, then value of $$\alpha$$ is

MHT CET 2023 11th May Morning Shift
31

Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\begin{array}{ccc}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$$ where each of $$a, b$$ and $$c$$ is either $$\omega$$ or $$\omega^2$$, then the number of distinct matrices in the set $$\mathrm{S}$$ is

MHT CET 2023 11th May Morning Shift
32

If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$\mathrm{A}$$ and $$|\mathrm{A}|=4$$, then $$\alpha$$ is equal to

MHT CET 2023 10th May Evening Shift
33

If $$B=\left[\begin{array}{lll}1 & \alpha & 2 \\ 1 & 2 & 2 \\ 2 & 3 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix A and $$|A|=5$$, then $$\alpha$$ is equal to

MHT CET 2023 10th May Morning Shift
34

If $$\left|\begin{array}{ccc}\cos (A+B) & -\sin (A+B) & \cos (2 B) \\ \sin A & \cos A & \sin B \\ -\cos A & \sin A & \cos B\end{array}\right|=0$$, then the value of $$B$$ is

MHT CET 2023 9th May Evening Shift
35

Let $$A=\left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & 1 & 3 \\ 1 & -2 & 1\end{array}\right], B=\left[\begin{array}{c}6 \\ 11 \\ 0\end{array}\right]$$ and $$X=\left[\begin{array}{l}a \\ b \\ c\end{array}\right]$$, if $$\mathrm{AX}=\mathrm{B}$$, then the value of $$2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}$$ is

MHT CET 2023 9th May Evening Shift
36

If $$A=\left[\begin{array}{cc}2 & -1 \\ -1 & 3\end{array}\right]$$, then the inverse of $$\left(2 A^2+5 A\right)$$ is

MHT CET 2023 9th May Morning Shift
37

If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$$, then $$(A B)^{-1}=$$

MHT CET 2022 11th August Evening Shift
38

Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if $$x y z=60$$ and $$8 x+4 y+3 z=20$$, then $$A$$.(adjA)

MHT CET 2022 11th August Evening Shift
39

If $$\mathrm{A}=\left[\begin{array}{cc}\lambda & \mathrm{i} \\ \mathrm{i} & -\lambda\end{array}\right]$$ and $$\mathrm{A}^{-1}$$ does not exist, then $$\lambda=$$ (where $$\mathrm{i}=\sqrt{-1}$$)

MHT CET 2021 24th September Evening Shift
40

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, and $$A(\operatorname{adj} A)=k I$$, then the value of $$(k+1)^4$$ is

MHT CET 2021 24th September Evening Shift
41

IF $$A X=B$$, where $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right], B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$$, then $$2 x+y-z=$$

MHT CET 2021 24th September Evening Shift
42

$$\text { If } A=\left[\begin{array}{ll} 2 & -2 \\ 2 & -3 \end{array}\right], B=\left[\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right] \text {, then }\left(B^{-1} A^{-1}\right)^{-1}=\text { ? }$$

MHT CET 2021 24th September Morning Shift
43

If $$A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & a \\ 2 & 4 & 7\end{array}\right]$$ and $$B=\left[\begin{array}{ccc}13 & 2 & b \\ -3 & -1 & 2 \\ -2 & 0 & 1\end{array}\right]$$ where matrix B is inverse of matrix A, then the value of a and b are

MHT CET 2021 24th September Morning Shift
44

For a $$3 \times 3$$ matrix $$\mathrm{A}$$, if $$\mathrm{A}(\operatorname{adj} \mathrm{A})=\left[\begin{array}{ccc}-10 & 0 & 0 \\ 0 & -10 & 2 \\ 0 & 0 & -10\end{array}\right]$$, then the value of determinant of A is

MHT CET 2021 24th September Morning Shift
45

If $$A=\left[\begin{array}{ccc}5 & 6 & 3 \\ -4 & 3 & 2 \\ -4 & -7 & 3\end{array}\right]$$, then cofactors of all elements of second row are respectively.

MHT CET 2021 23rd September Evening Shift
46

Which of the following matrices are invertible?

$$\begin{aligned} & \mathrm{A}=\left[\begin{array}{cc} 2 & 3 \\ 10 & 15 \end{array}\right], \mathrm{B}=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & -1 & 3 \\ 1 & 2 & 3 \end{array}\right], \mathrm{C}=\left[\begin{array}{lll} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 4 & 6 & 8 \end{array}\right], \mathrm{D}=\left[\begin{array}{lll} 2 & 4 & 2 \\ 1 & 1 & 0 \\ 1 & 4 & 5 \end{array}\right] \end{aligned}$$

MHT CET 2021 23rd September Evening Shift
47

If $$A=\left[\begin{array}{rr}2 & 3 \\ 5 & -2\end{array}\right]$$ and $$A^{-1}=K A$$, then $$K$$ is

MHT CET 2021 23th September Morning Shift
48

If $$\mathrm{A}=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, then $$\mathrm{A}(\operatorname{adj} \mathrm{A})=$$

MHT CET 2021 23th September Morning Shift
49

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right], B=\left[\begin{array}{l}1 \\ 1 \\ 2\end{array}\right]$$ and $$X=\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]$$ such that $$A X=B$$, then the value of $$x_1+x_2+x_3=$$

MHT CET 2021 23th September Morning Shift
50

If $$A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$$ and $$A$$ adj $$A=A A^T$$, then $$5 a+b=$$

MHT CET 2021 22th September Evening Shift
51

For an invertible matrix $$A$$, if $$A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \\ 0 & 20\end{array}\right]$$, then $$|A|=$$

MHT CET 2021 22th September Evening Shift
52

If $$A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{cc}1 & 2 \\ -3 & 1 \\ 0 & 2\end{array}\right]$$, then $$(A B)^{-1}$$

MHT CET 2021 22th September Evening Shift
53

If $$A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 3 \\ 1 & 2 & 1\end{array}\right]$$, then the value of determinant of $$A^{-1}$$ is

MHT CET 2021 22th September Morning Shift
54

If $$A = \left[ {\matrix{ k & 2 \cr { - 2} & { - k} \cr } } \right]$$, then A$$^{-1}$$ does not exists if k =

MHT CET 2021 22th September Morning Shift
55

The sum of three numbers is 6. Thrice the third number when added to the first number gives 7. On adding three times first number to the sum of second and third number we get 12. The product of these numbers is

MHT CET 2021 22th September Morning Shift
56

If $$A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$$, then $$\operatorname{adj} A=$$

MHT CET 2021 21th September Evening Shift
57

If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]$$ and $$A^{-1}=\frac{1}{2}\left[\begin{array}{ccc}1 & -1 & 1 \\ -8 & 6 & 2 c \\ 5 & -3 & 1\end{array}\right]$$, then values of a and c are respectively

MHT CET 2021 21th September Evening Shift
58

If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$, then $$A^{-1}=$$

MHT CET 2021 21th September Evening Shift
59

If $$F(\propto)=\left[\begin{array}{ccc}\cos \propto & -\sin \propto & 0 \\ \sin \propto & \cos \propto & 0 \\ 0 & 0 & 1\end{array}\right]$$, where $$\propto \in R$$, then $$[F(\propto)]^{-1}=$$

MHT CET 2021 21th September Morning Shift
60

If $$A=\left[\begin{array}{ccc}1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1\end{array}\right], \operatorname{adj} A=\left[\begin{array}{ccc}5 & x & -2 \\ 1 & 1 & 0 \\ -2 & -2 & y\end{array}\right]$$, then value of $$x+y$$ is

MHT CET 2021 21th September Morning Shift
61

$$\mathrm{A}^{-1}=\frac{-1}{2}\left[\begin{array}{cc}1 & -4 \\ -1 & 2\end{array}\right]$$, then $$2 A+I_2=\quad$$

where $$I_2$$ is a unit matrix of order 2

MHT CET 2021 21th September Morning Shift
62

The co-factors of the elements of second column of $$\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 2 & 1 \\ -1 & 3 & 4\end{array}\right]$$ are

MHT CET 2021 20th September Evening Shift
63

If $$A^{-1}=\left[\begin{array}{lll}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 5 & 5\end{array}\right]$$, then $$A=$$

MHT CET 2021 20th September Evening Shift
64

If $$A^{-1}=\left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$$ and $$B^{-1}=\left[\begin{array}{cc}1 & 0 \\ -3 & 1\end{array}\right]$$, then $$(A B)^{-1}=$$

MHT CET 2021 20th September Evening Shift
65

$$A(\propto)=\left[\begin{array}{cc}\cos \propto & \sin \propto \\ -\sin \propto & \cos \propto\end{array}\right]$$, then $$\left[A^2(\propto)\right]^{-1}=$$

MHT CET 2021 20th September Morning Shift
66

If inverse of $$\left[\begin{array}{ccc}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$$ does not exist, then $$x=$$

MHT CET 2021 20th September Morning Shift
67

If $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 1 & 2 & 1 \cr 3 & 2 & 6 \cr } } \right]$$ and A$$_{ij}$$ are cofactors of the elements a$$_{ij}$$ of A, then $${a_{11}}{A_{11}} + {a_{12}}{A_{12}} + {a_{13}}{A_{13}}$$ is equal to

MHT CET 2021 20th September Morning Shift
68

If $A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]$ and $A^2-5 A-6 I=0$, then $A^{-1}=$

MHT CET 2020 19th October Evening Shift
69

The cofactors of the elements of the first column of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$ are

MHT CET 2020 19th October Evening Shift
70

The matrix $$A=\left[\begin{array}{rrr}a & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2\end{array}\right]$$ is not invertible only if $$a=$$

MHT CET 2020 16th October Evening Shift
71

If $$A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right], \quad B=\left[\begin{array}{ll}1 & 0 \\ 3 & 1\end{array}\right]$$, then $$B^{-1} A^{-1}=$$

MHT CET 2020 16th October Evening Shift
72

The sum of the cofactors of the elements of second row of the matrix $$\left[\begin{array}{rrr}1 & 3 & 2 \\ -2 & 0 & 1 \\ 5 & 2 & 1\end{array}\right]$$ is

MHT CET 2020 16th October Morning Shift
73

If $$A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$$ and $$A^{-1}=\left[\begin{array}{rrr}3 & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2\end{array}\right]$$, then the values of $$\alpha$$ and $$\beta$$ are, respectively.

MHT CET 2020 16th October Morning Shift
74

If $A$ and $B$ are square matrices of order 3 such that $|A|=2,|B|=4$, then $|A(\operatorname{adj} B)|=\ldots$

MHT CET 2019 3rd May Morning Shift
75

If $A$ is non-singular matrix and $(A+I)(A-I)=0$ then $A+A^{-1}=$ .............

MHT CET 2019 2nd May Evening Shift
76

If $A=\left[\begin{array}{cc}1+2 i & i \\ -i & 1-2 i\end{array}\right]$, where $i=\sqrt{-1}$, then $A(\operatorname{adj} A)=\ldots$

MHT CET 2019 2nd May Evening Shift
77

If $A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right]$ and $A=A^{-1}$, then $x=\ldots \ldots$

MHT CET 2019 2nd May Morning Shift
78

If $A$ is non-singular matrix such that $(A-2 l)(A-4 I)=0$ then $A+8 A^{-1}=$ ..........

MHT CET 2019 2nd May Morning Shift
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