Matrix to the Power 10

I have to calulate A^10.

I have been given A =
(1 2
2 1)

and B =
(1 1
1 -1)

I have calculated that B^-1AB =
(3 0
0 1)

and I don't really understand what my notes mean to take it on from here. Help would be appreciated. :)

To find

You must find a diagonal matrix such that



In your case

and where is the eigenvectors of

So first thing to do is find the eigenvalues and eigenvectors of

(Nod)

It looks like you have been given that (Rofl) so use



As you have and

If that was a little to hard to follow then,



Just solve the RHS.