Match List - I with List - II. If $A = \begin{vmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{vmatrix}$

List - I	List - II
(A) $M_{23}$	(I) $-17$
(B) $A_{32} + a_{13}$	(II) $-1$
(C) A	(III) 0
(D) $a_{13}A_{12} + a_{23}A_{22} + a_{33}A_{32}$	(IV) 12

Choose the correct answer from the options given below :

The value (/s) of $x$ satisfying the matrix equation:

$x\begin{bmatrix}2x & 2\\3 & x\end{bmatrix}+2\begin{bmatrix}8 & 5x\\4 & 4x\end{bmatrix}=2\begin{bmatrix}(x^2+8) & 24\\10 & 6x\end{bmatrix}$ is/are:

If A and B are invertible matrices of order 3, $|A| = 2$ and $|(AB)^{-1}| = -\frac{1}{6}$, then the value of $|B|$ is :

If A is a square matrix of order $n$, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $A = \begin{bmatrix} 0 & x & x \\ 2y & y & -y \\ z & -z & z \end{bmatrix}$ such that $AA^T=2I$ (where I is an identity matrix of order 3), then which of the following are True?

A. $x^2=1, 3y^2=2$

B. $6y^2=4, 2z^2=3$

C. $9z^2=6, x^2=1$

D. $x^2:y^2:z^2 = 3:1:2$

Choose the correct answer from the options given below:

If $2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}$, then the value of $x-y$ is :

If A is an invertible matrix of order 3 and $|A|=7$, then the value of $|adj\ A|$ is: