- #1

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## Homework Statement

Given the matrix A=

-1/5 7/5

-3/5 -4/5

find A

^{43}.

## The Attempt at a Solution

It's obvious that I can't go and actually compute A

^{43}so there must be a more elegant way of doing this. The only notes I have on the subject is A

^{k}=P

^{-1}D

^{k}P, where D is a diagonal matrix. However, I have no clue what P is supposed to to, nor why this would work in the first place.