(A is invertible)
If A is a nxn matrix that is idempotent and invertible, then .
Let A be any nxn matrix such that A is idempotent and invertible. Then, by definition A satisfies the following properties,
and A can be written as the product of elementary matrices.
So, since we can say
...I don't really know how to finish this...
Should I use an equivalent condition for invertible matrices?