# What are Idempotents?

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

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Landau

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?

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

Landau

A= A^2 then B=B^2
This is what you need to prove.
A^2 = B^2 then (AB)^2 = AABB = A^2B^2 = A = b
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.