Question

Given a square matrix, A, how can I derive an expression for any particular element in A^n?

Answer 1

I solved my own question. (In my case it was a 2x2 matrix) So for anyone who might read this I used:

\[\lambda^n = c _{0} + c1\lambda\]

solved for c0 and c1. then used:

\[A ^{n} = c_{0} I_{2} + c_{1}A\]

to find each element in the matrix.