For a matrix $A$,the conditions $AI = A$ and $AA^T = I$ are true for:

If $X = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$,then the value of $X^n$ is

For the matrix $A = \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}$,find the values of $a$ and $b$ such that $A^{2} + aA + bI = 0$.

Let $A$ and $B$ be two symmetric matrices of the same order. Then,the matrix $AB - BA$ is

If $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $,then the values of $ x $ and $ y $ are:

If $A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix}$ and $B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix}$,then compute $3A - 5B$.