The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:

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 matrix has $24$ elements,what are the possible orders it can have? What if it has $13$ elements?

Find $X$ and $Y$,if $X+Y=\left[\begin{array}{ll}5 & 2 \\ 0 & 9\end{array}\right]$ and $X-Y=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]$.

If $A = \begin{bmatrix} 3 & 4 \\ 1 & -6 \end{bmatrix}$ and $B = \begin{bmatrix} -2 & 5 \\ 6 & 1 \end{bmatrix}$,then find $X$ such that $A + 2X = B$.

If $[m \ n] \begin{bmatrix} m \\ n \end{bmatrix} = [25]$ and $m < n$,then $(m, n) =$