If $M$ is a $3 \times 3$ matrix such that $(0\,1\,2) M = (1\,0\,0)$ and $(3\,4\,5) M = (0\,1\,0)$, then $(6\,7\,8) M$ is equal to

If a matrix has $24$ elements,what are the possible orders it can have? What if it has $13$ elements?

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

Compute the indicated products $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix} \begin{bmatrix} 2 & 3 & 4 \end{bmatrix}$.

If $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$,then $(BB^TA)^5$ is equal to

If $A = \begin{bmatrix} \sin \alpha & \cos \alpha \\ -\cos \alpha & \sin \alpha \end{bmatrix}$,then verify that $A^{\prime} A = I$.