# What are Idempotents?

1. May 4, 2010

### heidle12

First what are Idempotents?
Second, If A and B are simliar matrices, show that if A is idempotent then so is B.

2. May 5, 2010

### Landau

Re: idempotent

First, any definition can be found on the internet. An idempotent is an 'element' a such that a^2=a. So an idempotent matrix is a matrix A such that $A^2=A$.

Second, what have you tried?

3. May 5, 2010

### heidle12

Re: idempotent

A= A^2 then B=B^2
A^2 = B^2 then (AB)^2 = AABB = A^2B^2 = A = b
REALLY NOT SURE - NOT CONFIDENT IN MY THOUGHTS

4. May 5, 2010

### Landau

Re: idempotent

This is what you need to prove.
You can't assume that A^2=B^2. Moreover (AB)^2=ABAB, which is not the same as AABB.

The assumption is that A and B are similar. So first you have to know what that means. If you don't, look up the definition.