If $A'$ and $B'$ are the transpose matrices of the square matrices $A$ and $B$ respectively,then $(AB)'$ is equal to:

If the matrix $A$ is both symmetric and skew-symmetric,then

$A, B, C, D$ are square matrices such that $A+B$ is symmetric,$A-B$ is skew-symmetric and $D$ is the transpose of $C$. If $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5\end{array}\right]$ and $C=\left[\begin{array}{ccc}0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1\end{array}\right]$,then the matrix $B+D=$

If $A$ is a skew symmetric matrix,then $A^{2021}$ is

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,

Show that the matrix $B^{\prime}AB$ is symmetric or skew-symmetric according as $A$ is symmetric or skew-symmetric.