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 . . . . . . .

Suppose $A$ and $B$ are two square matrices of the same order. If $A$ and $B$ are symmetric matrices, then $AB - BA$ is

If the matrix $A = \begin{bmatrix} 0 & a & a \\ 2b & b & -b \\ c & -c & c \end{bmatrix}$ is orthogonal, then the values of $a, b, c$ are

Identify the incorrect statement in respect of two square matrices $A$ and $B$ conformable for sum and product.

Show that the matrix $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew-symmetric matrix.

$A=\begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$ and $B=\begin{bmatrix} x & y \\ 1 & 2 \end{bmatrix}$ are two matrices such that $(A+B)(A-B)=A^2-B^2$. If $C=\begin{bmatrix} x & 2 \\ 1 & y \end{bmatrix}$, then $\operatorname{Trace}(C)=$