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Suppose $A$ is a square matrix such that $A^2=6A$.

Which of the following matrices, if any, is an idempotent matrix?

A

$6A$

B

$\cfrac{1}{6}A$

C

$\sqrt{6}A$

D

$\cfrac{1}{\sqrt{6}}A$

E

None of this matrices are idempotent

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