If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{\prime} = I$,then the value of $\alpha$ is . . . . . . .

Which one of the following statements is correct regarding skew-symmetric matrices?

Let $A+2 B=\left[\begin{array}{ccc}1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1\end{array}\right]$ and $2 A - B =\left[\begin{array}{ccc}2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2\end{array}\right] .$ If $\operatorname{Tr}( A )$ denotes the sum of all diagonal elements of the matrix $A ,$ then $\operatorname{Tr}( A )-\operatorname{Tr}( B )$ has value equal to

If $A$ is a square matrix,then $A + A^T$ is:

If $A^{\prime}=\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B=\begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}$,then verify that $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.

If $A = \begin{bmatrix} -2 \\ 4 \\ 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & -6 \end{bmatrix}$,verify that $(AB)^{\prime} = B^{\prime} A^{\prime}$.