# Intro Linear Algebra proof

• July 1st 2009, 11:01 AM
Danneedshelp
Intro Linear Algebra proof
If A is a nxn matrix that is idempotent and invertible, then $A=I_{n}$.

Let A be any nxn matrix such that A is idempotent and invertible. Then, by definition A satisfies the following properties,

$A^{2}=A$ and A can be written as the product of elementary matrices.

So, since $A^{2}=A$ we can say $A^{2}=E_{k}^{-1}...E_{1}^{-1}$

...I don't really know how to finish this...

Should I use an equivalent condition for invertible matrices?
• July 1st 2009, 11:13 AM
Bruno J.
$A^2=A$

$A^{-1}A^2=A^{-1}A$ (A is invertible)

$A=I$
• July 1st 2009, 11:23 AM
Danneedshelp
Wow...I feel dumb. Thanks alot. I figured I had to use the elementary matrices since thats all the section was about ha.