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This is not a homework question.

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

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.

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# Inverse of Change of Basis Matrix

Can you offer guidance or do you also need help?

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