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 $A = \left( {\begin{array}{*{20}{c}}
{\alpha  – 1}\\
0\\
0
\end{array}} \right),\,\,\,B = \left( {\begin{array}{*{20}{c}}
{\alpha  + 1}\\
0\\
0
\end{array}} \right)$ be two matrices, then $AB^T$ is a non-zero matrix for $\left| \alpha  \right|$ not equal to

Given $A$ and $C$ are involutary matrices and $B$ is a non-singular matrix, then $(AB^{-1}C)^{-1}$ is equal to –

If  $A$  is a square matrix for which ${a_{ij}} = {i^2} – {j^2}$, then $A$ is

If  $A$  and  $B $ be symmetric matrices of the same order, then $AB – BA$ will be a