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## Homework Statement

Suppose matrices A and B are similar. Explain why they have the same rank.

## Homework Equations

## 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.