1. The problem statement, all variables and given/known data Suppose matrices A and B are similar. Explain why they have the same rank. 2. Relevant equations 3. The attempt at a solution So if A and B are similar, then there is some invertible matrix P such that B = P^-1AP. I have been trying to find some way to relate rank(A) to rank(P^-1AP) but I can't figure it out. I feel like maybe i'm missing some intuition about this. This comes at the end of a section about linear transformations. Thank you to anyone who can help.