Find $x$ and $y,$ if $2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix}$

If $\omega \neq 1$ is a cube root of unity and $H = \begin{bmatrix} \omega & 0 \\ 0 & \omega \end{bmatrix}$,then $H^{70}$ is equal to:

If $A$ and $B$ are two matrices,such that $AB = B$ and $BA = A$,then $A^2 + B^2$ is equal to:

The matrix $\begin{bmatrix} 2 & 5 & -7 \\ 0 & 3 & 11 \\ 0 & 0 & 9 \end{bmatrix}$ is known as:

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$ and $A^3 = \begin{bmatrix} \cos 3 \theta & m \\ n & \cos 3 \theta \end{bmatrix}$,the values of $m$ and $n$ respectively are

If $I=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $P=\begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2 \end{bmatrix}$, then the matrix $P^{3}+2P^{2}$ is equal to