Let $A$ be a skew-symmetric matrix of odd order,then $|A|$ is equal to

If the matrix $A = \begin{bmatrix} 0 & a & a \\ 2b & b & -b \\ c & -c & c \end{bmatrix}$ is orthogonal, then the values of $a, b, c$ are

Find $\frac{1}{2}(A+A^{\prime})$ and $\frac{1}{2}(A-A^{\prime}),$ when $A=\left[\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right].$

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

If $A = \begin{bmatrix} -2 \\ 4 \\ 5 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & -6 \end{bmatrix}$,verify that $(AB)^{\prime} = B^{\prime} A^{\prime}$.

If $A=\begin{bmatrix}-1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1\end{bmatrix}$ and $B=\begin{bmatrix}-4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1\end{bmatrix}$,then verify that $(A+B)^{\prime}=A^{\prime}+B^{\prime}$.