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

Show that the matrix $A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix}$ is a skew-symmetric matrix.

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?

If $A$ is a $3 \times 3$ order skew-symmetric matrix,then $|A|$ is equal to:

Express the matrix $B=\left[\begin{array}{rrr}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]$ as the sum of a symmetric and a skew symmetric matrix.

If $A = \begin{bmatrix} 1 & -2 \\ 5 & 3 \end{bmatrix}$,then $A + A^T$ equals: