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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 $M^{-1}BM$

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    Hint: $\lambda I = M^{-1}(\lambda I) M$.2011-10-05

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A small hint: In the expression $\det(A-\lambda I)$ you can use the given fact that $A=M^{-1}BM$ of course, but also that $I=M^{-1}IM$.

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    @Colin: If you're happy with Hans's answer, please remember to click the checkmark to the left of his answer, so that the software considers this resolved. :)2011-10-05