# Inverse of Change of Basis Matrix

1. Aug 17, 2011

### CantorSet

Hi everyone,

This is not a homework question.

Let $B_1$ and $B_2$ be orthonormal bases. Let $M$ be the change of basis matrix from $B_1$ to $B_2$. Then, is the inverse of $M^{-1}$ also a change of basis matrix? Namely, from $B_2$ to $B_1$?

At an intuitive level, I just assumed that was the case. Until I did some toy examples and it didn't seem to work out.

What do you guys think?

EDIT: Nevermind, I found a mistake in my calculation.

Last edited: Aug 17, 2011