Let M=
[4 -2]
[1 1]
Find formulas for the entries of M^n, where n is a positive integer.
You need to diagonalize the matrix.
Read: Matrix Diagonalization -- from Wolfram MathWorld
So if $\displaystyle M=PDP^{-1}$ where D is diagonal then $\displaystyle M^m=PD^mP^{-1}$. Try it.