The matrix $A = \frac{1}{3}\left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ – 2}\\{ – 2}&2&{ – 1}\end{array}} \right]$is

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

Let $A\, = \,\left( {\begin{array}{*{20}{c}}
0&{2q}&r\\
p&q&{ – r}\\
p&{ – q}&r
\end{array}} \right)$. If $A{A^T}\, = \,{I_3},\,\left| p \right|$ then $\left| p \right|$ is

If $A=\left(\begin{array}{cc}0 & \sin \alpha \\ \sin \alpha & 0\end{array}\right)$ and $\operatorname{det}\left(A^{2}-\frac{1}{2} I\right)=0,$ then a possible value of $\alpha$ is

Find the transpose of the following matrices : $\left[\begin{array}{ccc}-1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1\end{array}\right]$