Invertible matrices problem

• Feb 28th 2010, 12:59 PM
temaire
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.
• Feb 28th 2010, 01:15 PM
Defunkt
Quote:

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)\$ ?
• Feb 28th 2010, 01:31 PM
temaire
Quote:

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

That would be the identity matrix \$\displaystyle I\$ right?
• Feb 28th 2010, 02:29 PM
Defunkt
Quote:

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)\$ ?
• Feb 28th 2010, 02:32 PM
temaire
Ok I think I got it.

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

Thanks for the help.