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

For any square matrix $A$,$AA^T$ is a

If $A$ and $B$ are symmetric matrices of the same order,then show that $AB$ is symmetric if and only if $A$ and $B$ commute,that is $AB = BA$.

$A, B, C, D$ 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 $A$ and $B$ are skew-symmetric matrices of the same order,then $(AB)^{\prime} =$ . . . . . . .

If $A$ and $B$ are square matrices of the same order and $B$ is a skew-symmetric matrix,then $A^{\prime} B A$ is