If $P = \begin{bmatrix} 1 & 0 \\ 1/2 & 1 \end{bmatrix}$,then $P^{50}$ is:

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

Which of the following statements is true regarding matrix multiplication?

If $A=\left[\begin{array}{rrr}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$,$B=\left[\begin{array}{rr}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ and $C=\left[\begin{array}{rrrr}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right]$,find $A(BC)$,$(AB)C$ and show that $(AB)C=A(BC)$.

Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A^{2}$ is $1,$ then the possible number of such matrices is

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$, then find $A^8$. (in $B$)