1
MHT CET 2023 13th May Morning Shift
+2
-0

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

A
0
B
$$-$$2
C
4
D
3
2
MHT CET 2023 12th May Evening Shift
+2
-0

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

A
$$-$$1
B
1
C
5
D
$$-$$5
3
MHT CET 2023 12th May Morning Shift
+2
-0

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

A
$$\frac{8}{11}$$
B
$$\frac{4}{11}$$
C
$$\frac{-8}{11}$$
D
$$\frac{-4}{11}$$
4
MHT CET 2023 11th May Evening Shift
+2
-0

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 $$\mathrm{B}^{-1}=$$

A
$$-\mathrm{A}$$
B
$$\operatorname{adj} \mathrm{A}$$
C
$$\mathrm{-I}$$
D
$$-\operatorname{adj} \mathrm{A}$$
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