Question
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
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