**Exercise 5.**
This software computes the order of elements in the \(GL(2,Z_p)\).
Enter several choices for matrices \(A\) and \(B\). The software
returns \(|A|\),\(|B|\), \(|AB|\), \(|BA|\), \(|A^{-1}BA|\) and
\(|B^{-1}AB|\). Do you see and relationship between \(|A|\),\(|B|\),
and \(|AB|\)? Do you see any relationship between \(|AB|\) and \(|BA|\)?
Make a conjecture about this relationship. Test your conjecture for
several other choices for \(A\) and \(B\). Do you see any relationship
between \(|B|\) and \(|A^{-1}BA|\)? Do you see any relationship between
\(|A|\) and \(|B^{-1}AB|\)? Make a conjecture about this relationship.
Test your conjecture for several other choices for \(A\) and \(B\).

Please enter the entries of \(A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\), \(B = \begin{bmatrix} e & f \\ g & h \end{bmatrix}\), and a prime \(p\).