Can someone please help me. I am not sure to work the following matrices.

Question

If A^4 =

-3 4
-4 5

and A^5=

4 -5
5 -6

What is A? Can you show me how you got this?

Thank you so much ;)

Answer 1

well, A^5 = A^4 * A
So, A = A^5 * (A^4)^-1

(A^4)^-1 =
5 -4
4 -3

So, A =
4 -5 * 5 -4
5 -6 4 -3
=
0 -1
1 -2