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## 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

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