# True or False?

Algebra Level 4

If $$A$$ is any invertible $$2\times 2$$ matrix, then there must exist two perpendicular unit vectors $$v$$ and $$w$$ such that the vectors $$Av$$ and $$Aw$$ are perpendicular as well.

Bonus Question: Can you generalize to 3 or even $$n$$ dimensions?

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