If $A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}$ and $\alpha, \beta \in \mathbb{R}$ are such that $\alpha A^2 - \beta A = 2I$, then $\alpha^2 + \beta =$

For the matrices $A$ and $B$,verify that $(AB)^{\prime} = B^{\prime}A^{\prime}$ where $A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix}$.

The number of all $3 \times 3$ matrices $A$,with entries from the set $\{-1, 0, 1\}$ such that the sum of the diagonal elements of $AA^{T}$ is $3$,is

Which of the following statements is true regarding matrix multiplication?

Let $A = \begin{bmatrix} b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2 \end{bmatrix}$. If $a = \sin \frac{\pi}{6}$,$b = \cos \frac{\pi}{4}$,and $c = \cot \frac{\pi}{2}$,then $A$ is:

If $I$ is a unit matrix,then $3I$ will be