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

If $A = \begin{bmatrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{bmatrix}$ and $A + A^{T} = I$, where $I$ is the $2 \times 2$ identity matrix and $A^{T}$ is the transpose of $A$, then the value of $\theta$ is:

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

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 $(A+B)^{\prime}=A^{\prime}+B^{\prime}$.

Let $A, B, C$ be $3 \times 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric. Consider the statements:
$(S1): A^{13} B^{26} - B^{26} A^{13}$ is symmetric
$(S2): A^{26} C^{13} - C^{13} A^{26}$ is symmetric
Then,

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 $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.