Let $A = \left[ {\begin{array}{*{20}{c}}
p&{13}\\
{ – 13}&p
\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}
{4q}&{85}\\
{ – 2}&1
\end{array}} \right]$  where  $p,q \in N$. It is given that $\left| A \right| = \left| B \right|$ and  $p,q \in[1,1000]$. Then total number of ordered pairs $(p,q)$ is

If $[m\ n]\left[ {\begin{array}{*{20}{c}}m\\n\end{array}} \right] = [25]$ and $m< n$, then $(m, n) =$

Let $A$ and $B$ be two $3 \times 3$ real matrices such that $\left(A^{2}-B^{2}\right)$ is invertible matrix. If $A^{5}=B^{5}$ and $A^{3} B^{2}=A^{2} B^{3}$, then the value of the determinant of the matrix $A^{3}+B^{3}$ is equal to:

If the matrix $\left[ {\begin{array}{*{20}{c}}0&1&{ – 2}\\{ – 1}&0&3\\\lambda &{ – 3}&0\end{array}} \right]$ is singular, then $\lambda $=

If $2X – \left[ {\begin{array}{*{20}{c}}1&2\\7&4\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}3&2\\0&{ – 2}\end{array}} \right]$, then $X$  is equal to