If $A = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{bmatrix}$,then $A^{4}$ is equal to

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,then ${A^2} = $

If $x\begin{bmatrix} 3 \\ 2 \end{bmatrix} + y\begin{bmatrix} 1 \\ -1 \end{bmatrix} = \begin{bmatrix} 15 \\ 5 \end{bmatrix}$,then the values of $x$ and $y$ are:

Compute the indicated products $\left[\begin{array}{lll}2 & 3 & 4 \\ 3 & 4 & 5 \\ 4 & 5 & 6\end{array}\right]\left[\begin{array}{ccc}1 & -3 & 5 \\ 0 & 2 & 4 \\ 3 & 0 & 5\end{array}\right]$

If $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$,then which of the following statements is not correct?

If $A$ is a $2 \times 2$ matrix and $a_{ij} = \frac{i + 2j^2}{3}$,then find the matrix $A = [a_{ij}]_{2 \times 2}$.