# Linear Algebra- Diagonal Matrix

Roni1985

## 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

## 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

D2=D

b) I solved this part

Also,
is (AB)2= A2*B2
or
(AB)2=B2*A2
?

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