Find the value of $x, y$ and $z$ from the following equation: $\begin{bmatrix} x+y+z \\ x+z \\ y+z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix}$

If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then ${A^4} = $

If $A=\begin{bmatrix} b & a & 0 \\ c & 0 & b \\ a & a & b \end{bmatrix}$ and $B=\begin{bmatrix} 0 & a & b \\ b & 0 & c \\ b & a & a \end{bmatrix}$ are two matrices such that $AB=\begin{bmatrix} 2 & 2 & 7 \\ 1 & 8 & 5 \\ 3 & 6 & 10 \end{bmatrix}$,then $a^2+b^2+c^2=$

If $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $,then the values of $ x $ and $ y $ are:

If $M = \begin{bmatrix} \frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2} \end{bmatrix}$,then which of the following matrices is equal to $M^{2022}$?

The matrix $A = \frac{1}{3}\begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ -2 & 2 & -1 \end{bmatrix}$ is