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

Express the following matrix as the sum of a symmetric and a skew-symmetric matrix: $\left[\begin{array}{rrr}6 & -2 & 2 \\ -2 & 3 & -1 \\ 2 & -1 & 3\end{array}\right]$

For a given matrix $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$,which of the following statements holds true?

$A=\begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}$ 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 $\operatorname{Trace}(C)=$

If $A = \begin{bmatrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{bmatrix}$,then $A \cdot A^{\prime}$ is

If $A$ is a $3 \times 3$ order skew-symmetric matrix,then $|A|$ is equal to: