# Invertible matrices problem

• Feb 28th 2010, 01:59 PM
temaire
Invertible matrices problem
Show that the square matrix $2N - I$ is its own inverse if $N^{2} = N$

I really don't know where to start here. All I know is that I have to show that $2N - I = (2N - I)^{-1}$.

Any help is appreciated.
• Feb 28th 2010, 02:15 PM
Defunkt
Quote:

Originally Posted by temaire
Show that the square matrix $2N - I$ is its own inverse if $N^{2} = N$

I really don't know where to start here. All I know is that I have to show that $2N - I = (2N - I)^{-1}$.

Any help is appreciated.

What is $(2N-I)(2N-I)$ ?
• Feb 28th 2010, 02:31 PM
temaire
Quote:

Originally Posted by Defunkt
What is $(2N-I)(2N-I)$ ?

That would be the identity matrix $I$ right?
• Feb 28th 2010, 03:29 PM
Defunkt
Quote:

Originally Posted by temaire
That would be the identity matrix $I$ right?

This is what you need to show.

What do you get when you expand $(2N-I)(2N-I)$ ?
• Feb 28th 2010, 03:32 PM
temaire
Ok I think I got it.

If I expand it, I will get the identity matrix.

Thanks for the help.