If $A$ and $B$ are two matrices and $(A + B)(A - B) = A^2 - B^2$,then

$\begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix} \begin{bmatrix} 2 & 1 & -1 \end{bmatrix} = $

Let the matrix $A = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}$ satisfy $A^n = A^{n-2} + A^2 - I$ for $n \geq 3$. Then the sum of all the elements of $A^{50}$ is:

If $A$ and $B$ are two matrices such that $AB$ is an identity matrix and the order of matrix $B$ is $3 \times 4$,then the order of matrix $A$ is

If $P = \begin{bmatrix} \cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4} \end{bmatrix}$ and $X = \begin{bmatrix} \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{bmatrix}$, then $P^3 X$ is equal to:

If $2\begin{bmatrix} 5 & x \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5 \\ 7 & 0 \end{bmatrix}$,then find the values of $x$ and $y$.