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## Homework Statement

if A is similar to B with P^-1 A P = B and x is an eigenvector of A, prove that P^-1x is an eigenvector of B

## Homework Equations

## The Attempt at a Solution

so far I did this:

A = PBP^-1

Ax = PBP^-1x

P^-1Ax = BP^-1x

B^-1P^-1Ax = P^-1x

is that sufficient to prove that P^-1x is the eigenvector of B? ??

I don't think so .. if yes please explain how.. or else please give a proper "proof" .

I guess the reason I don't think this is right is becaues I am not able to bring it to the format of Ax = tx where t is an eigenvalue and x is the eigenvector. Any help would be appreciated.

Final exam on tuesday ... :(