Homework Help: Linear Algebra- Diagonal Matrix

1. Mar 6, 2010

Roni1985

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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
?

Last edited: Mar 6, 2010
2. Mar 6, 2010

Dick

You just need to make up some notation. Let diag(a1,a2,...an) be the matrix whose diagonal entries are a1, a2... Now what diag(a1,a2,...an)*diag(b1,b2,...bn)? (AB)^2 generally isn't equal to either A^2*B^2 or B^2*A^2. It's just ABAB.

3. Mar 6, 2010

Roni1985

oh, right , it works ...
thanks a lot for the help ....