If matrix $A = \begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$ and $A' = A$, then :

If A is a square matrix of order $3 \times 3$ and $|A| = 4$. The value of $|(adjA).A|$ is

If $A = \begin{bmatrix} 0 & 2 & -3 \\ y & 0 & -1 \\ z & x & 0 \end{bmatrix}$ is skew symmetric matrix, then $x^3 + y^3 + z^3 - 3xyz$ is equal to :

If $x, y$ and $z$ are non-zero distinct numbers, then $\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}$ is equal to

If $A=\begin{bmatrix} 1 & 0 \\ -1 & 5 \end{bmatrix}$ and I is indentity matrix of order 2, then which of following statements are TRUE?

A. $A^2-6A-mI=0$ if $m=-5$.

B. $A^2-6A+mI=0$ if $m=-5$.

C. $A$ is a non-singular matrix.

D. $A^2=A$

Choose the correct answer from the options given below:

Let $A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2 \end{bmatrix}$. $M_{ij}$ and $A_{ij}$ respectively denote the minor and cofactor of an element $a_{ij}$ of matrix $A = [a_{ij}]$

(A) $M_{23} = 6$

(B) $A_{22} = -8$

(C) $A_{13} = 7$

(D) $M_{32} = -5$

Choose the correct answer from the options given below:

$A = \begin{bmatrix} 1/3 & 2 \\ 0 & 2x - 3 \end{bmatrix}$ & $B = \begin{bmatrix} 3 & 6 \\ 0 & -1 \end{bmatrix}$ If $AB = I$ (Where I is an identity matrix of order 2) , then value of x is