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

$P$ is an orthogonal matrix and $A$ is a periodic matrix with period $4$,and $Q = PAP^T$. Then $X = P^TQ^{2005}P$ will be equal to

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

If $A$ and $B$ are symmetric matrices,prove that $AB - BA$ is a skew-symmetric matrix.

If $A$ and $B$ are symmetric matrices,then $ABA$ is

The trace of the matrix $A = \begin{bmatrix} 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$ is defined only for square matrices. If we consider the matrix $A = \begin{bmatrix} 1 & -5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{bmatrix}$,what is its trace?