Let $A = \begin{bmatrix} -3 & 2 \\ 1 & 4 \end{bmatrix}$. If $A^2 - 2A + I = \begin{bmatrix} 18 & p \\ q & 11 \end{bmatrix}$, find the values of $p$ and $q$.

If $A$ is an $m \times n$ matrix and $B$ is a matrix such that both $AB$ and $BA$ are defined,then the order of $B$ is

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then $AB = $

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

Let $A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}$,$x \in \mathbb{R}$ and $A^{4} = [a_{ij}]$. If $a_{11} = 109$,then $a_{22}$ is equal to

$A=\left[\begin{array}{ccc}a^2 & 15 & 31 \\ 12 & b^2 & 41 \\ 35 & 61 & c^2\end{array}\right]$ and $B=\left[\begin{array}{ccc}2 a & 3 & 5 \\ 2 & 2 b & 8 \\ 1 & 4 & 2 c-3\end{array}\right]$ are two matrices such that the sum of the principal diagonal elements of both $A$ and $B$ are equal,then the product of the principal diagonal elements of $B$ is