1. ## Invertible matrices problem

Show that the square matrix $\displaystyle 2N - I$ is its own inverse if $\displaystyle N^{2} = N$

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

Any help is appreciated.

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

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

Any help is appreciated.
What is $\displaystyle (2N-I)(2N-I)$ ?

3. Originally Posted by Defunkt
What is $\displaystyle (2N-I)(2N-I)$ ?
That would be the identity matrix $\displaystyle I$ right?

4. Originally Posted by temaire
That would be the identity matrix $\displaystyle I$ right?
This is what you need to show.

What do you get when you expand $\displaystyle (2N-I)(2N-I)$ ?

5. Ok I think I got it.

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

Thanks for the help.