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

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 the matrix product $AB = O$,where $O$ is the null matrix,then which of the following is necessarily true?

If $A$ and $B$ are square matrices of order $3 \times 3$,$A$ is non-singular,and $AB = O$,then $B$ is a:

Let $A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1 \end{bmatrix}$ and $B = 7A^{20} - 20A^{7} + 2I$,where $I$ is an identity matrix of order $3 \times 3$. If $B = [b_{ij}]$,then $b_{13}$ is equal to $....$

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3 \end{bmatrix}$ and $B$ is a matrix such that $AB = BA$. If $AB$ is not an identity matrix,then the matrix that can be taken as $B$ is: