Proof of Nonsingular Matrices: Linear Algebra

[Mdhiggenz]

Homework Statement

http://i48.tinypic.com/2qu14ax.jpg

Can you guys explain whether or not my proof would be sufficient. My thought process was to start with the definition.

So if A is nonsingular is means that A has an inverse such that

A=A^-. I used that same thinking for B. B=B^-

Then using the question which states. IF A and B are nonsingular nxn matrices then AB is also nonsingular and (AB)^-=A^-B^-

I thought it would be easier to prove the right side so I started with AB=A^-B^-

and used the relationship A=A^- and B=B^- to show that both sides are equal. However I found the proof online, and they did something slightly different.

Am I incorrect, if so where did I go wrong in my thinking?

Thanks

Homework Equations

The Attempt at a Solution

 

[dx]

Non-singular does not mean that A = A^-1

It means that there is an inverse A^-1 such that AA^-1 = A^-1A = I

 

[dx]

And (AB)^-1 = B^-1A^-1, not A^-1B^-1