(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that two similar matrices A and B share the same determinants, WITHOUT using determinants

2. The attempt at a solution

A previous part of this problem not listed was to show they have the same rank, which I was able to do without determinants. The problem is I can't think of how to show they have the same eigenvalues without going to the characteristic polynomial (derived from the determinant of |A-lamba*I|. My other idea was to think of both A and B as the same linear map with respect to a different basis. After that I draw a blank.

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# Similar matrices = Same Eigenvalues (NO DETERMINANTS!)

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