Alright, I've been trying to work this linear algebra problem out for a bit and I don't seem to be getting anywhere. The problem is this:
Assume that $A=M^{-1}BM$. Show that $\det(A-\lambda I)=\det(B-\lambda I)$.
So my instincts tell me that this has something to do with the fact that $A^n$ can be expressed as $M^{-1}BM$