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

If $A=\left[\begin{array}{rrr}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{rrr}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{array}\right],$ then verify that $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.

Which of the following is a nilpotent matrix?

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

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 square matrix $A$,if $A = B + \frac{C}{2}$,where $B$ is a skew-symmetric matrix and $C$ is a symmetric matrix,then $C = $ . . . . . . .