Find the number of $3 \times 3$ matrices having all elements either $2$ or $9$.

If $m[-3, 4] + n[4, -3] = [10, -11]$, then $3m + 7n$ is equal to

If $P = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}$, then $P^5$ is equal to

Let $A=\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 3 & 4\end{array}\right]$,$B=\left[\begin{array}{ccc}4 & 0 & -3 \\ -1 & -2 & -3\end{array}\right]$ and $C=\left[\begin{array}{cccc}2 & -3 & 0 & 1 \\ 5 & -1 & -4 & 2 \\ -1 & 0 & 0 & 3\end{array}\right]$,what is $A^T B$ ?

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^n$ (where $n \in N$) equals

If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined,then