Question

(5A (with T on top) ) to the power of -1 = -3 -1
5 2

find A

Answer 1

basically its the inverse of transpose of A x 5 gives that 2x2 matrix

Answer 2

I hope this is right, I haven't done this in quite a while...
Take the inverse again to undo the inverse on the other side, which gives you-->
\[\left[\begin{matrix}-2 & -1 \\ 5 & 3\end{matrix}\right]\]

Take the transpose of this to undo the transpose on the other side and divide by 5-->
\[\left[\begin{matrix}-2/5 & 1 \\ -1/5 & 3/5\end{matrix}\right]\]