Eigenvalues -prove or refute Hey guys, I need to prove or refute that once given an eigenvalue t of a matrix AB and B is invertible, so t is also eigenvalue of A. I believe it's not true, but sadly beliefs are not enough in math : ) Thank you.

Let $A=B^{-1}$, then $t=1$. Clearly there are invertible matrices $B$ which don't have $1$ as an eigenvalue.