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## Homework Statement

Let D be an n x n diagonal matrix whose diagonal entries are either 0 or 1

a) Show that D is idempotent

b) Show that if X is a nonsingular matrix and A=XD(X)

^{-1}, then A is idempotent

## Homework Equations

## The Attempt at a Solution

a) I tried it, and it works for a specific matrix, say 3x3... but I don't know if it's really a proof.

I need to show that

D

^{2}=D

b) I solved this part

Also,

is (AB)

^{2}= A

^{2}*B

^{2}

or

(AB)

^{2}=B

^{2}*A

^{2}

?

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