1
MHT CET 2021 24th September Morning Shift
+2
-0

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

A
$$\mathrm{a}=-5, \mathrm{~b}=7$$
B
$$\mathrm{a=7, b=-5}$$
C
$$\mathrm{a=-7, b=5}$$
D
$$\mathrm{a}=5, \mathrm{~b}=-7$$
2
MHT CET 2021 24th September Morning Shift
+2
-0

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

A
100
B
$$-$$1000
C
$$-$$10
D
20
3
MHT CET 2021 23rd September Evening Shift
+2
-0

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.

A
$$-39,3,11$$
B
$$-39,27,11$$
C
$$39,-3,-11$$
D
$$39,-27,11$$
4
MHT CET 2021 23rd September Evening Shift
+2
-0

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}

A
both A and B
B
only C
C
only A
D
only D
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