# Homework Help: Linear Algebra Proof involving idempotency

1. Sep 24, 2014

### PsychonautQQ

1. The problem statement, all variables and given/known data
I = Identity matrix
Suppose that A^2 = A. Prove that I - 2A = (I - 2A)^-1

2. Relevant equations
ahh don't know what to put here

3. The attempt at a solution
So I have to prove this thing is it's own identity... interesting..

I - 2A = I - 2A^2

(I - 2A^2)*(I - 2A)^-1 = I

Distributive law?
Idk honestly this is all I have gotten.. And it's probably not the right direction, just trying to put all the information I know into one line I guess. Any Mathamavericks out there wanna help a noob out?

2. Sep 24, 2014

### Staff: Mentor

To show that A and B are inverses -- IOW, that B = A-1 -- show that AB = I.

3. Sep 25, 2014

### PsychonautQQ

Isn't that what I set up? I don't know how to solve it

4. Sep 25, 2014

### Dick

You want to show (1-2A) is its own inverse. I.e. (1-2A)*(1-2A)=I.

5. Sep 25, 2014

### Staff: Mentor

What you wrote, Psychonaut, was (1-2A)*(1-2A)-1=I. Do you see the difference?