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## Homework Statement

SUppose A and B are nxn matrices in the complex field and that A is unitarily similar to B.

## Homework Equations

Show that A

^{k}is unitarily similar to B

^{k}for all k=1,2,3,..

## The Attempt at a Solution

I used induction to show its true for k=1 which it is.

Then for k=n+1,

A

^{n+1}=(U

^{*})

^{n+1}B

^{n+1}U

^{n+1}

A

^{n}A=(U

^{n})

^{*}(U

^{*})B(B

^{n)}U

^{n}U.

That is as far as i got, any help?