1. ## Matrix Entries Formula

Let M=

[4 -2]
[1 1]

Find formulas for the entries of M^n, where n is a positive integer.

2. You need to diagonalize the matrix.
Read: Matrix Diagonalization -- from Wolfram MathWorld

So if $M=PDP^{-1}$ where D is diagonal then $M^m=PD^mP^{-1}$. Try it.