If $A$ is an involutory matrix and $I$ is the unit matrix of the same order,then $(I - A)(I + A)$ is

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

If $m[-3, 4] + n[4, -3] = [10, -11]$,then $3m + 7n$ is equal to

If $A=\left[\begin{array}{rrr}0 & 6 & 7 \\ -6 & 0 & 8 \\ 7 & -8 & 0\end{array}\right]$,$B=\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 2 \\ 1 & 2 & 0\end{array}\right]$,and $C=\left[\begin{array}{c}2 \\ -2 \\ 3\end{array}\right]$. Calculate $AC$,$BC$,and $(A + B)C$. Also,verify that $(A+B)C = AC + BC$.

If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$,then $(A+I)^3 + (A-I)^3 = \dots$

The value of $\cos \alpha$ is . . . . . . if $A+A^{\prime}=I$,where $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$.