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1) If B = P^-1AP and let X be an eigenvector of A corresponding to the eigenvalue y. Show that y is an eigenvalue of B and find a corresponding eigenvector.

This is what i did.

AX=yI and since B = P^-1Ap -> A = PBP^-1

so (PBP^-1)X=yI

Now this is the part where i get lost. Am i on the right track?

2) If A and B are nxn matrices, A is invertable, show that BA is similar to AB.

So BA = P^-1ABP because BA is similar to AB. But im kinda lost now. I'm sure i have to do something with the fact that A is invertable. Umm... A^-1....