Invertible matrices problem

**temaire** · February 28th 2010, 12:59 PM

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.

**Defunkt** · February 28th 2010, 01:15 PM

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 $(2N-I)(2N-I)$ ?

**temaire** · February 28th 2010, 01:31 PM

Originally Posted by Defunkt

What is $(2N-I)(2N-I)$ ?

That would be the identity matrix $I$ right?

**Defunkt** · February 28th 2010, 02:29 PM

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 $(2N-I)(2N-I)$ ?

**temaire** · February 28th 2010, 02:32 PM

Ok I think I got it.

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

Thanks for the help.

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