Prove that if A is nonsingular then the transpose of A is nonsingular.

[seang]

I haven't written a proof in 8 years. Linear Algebra proofs are going to be the death of me. I honestly don't know where to begin. I read a sort of primer on proof writing, but I could use a human walk through or some help.

So far, I have:

there exists a B such that AB = BA = I.


then sometime later:

(A^T)B = B(A^T) = I

Beyond this I have no idea. I'm going to visit my prof tomorrow and see what he has to say. The trouble is, is that his english is fair to poor. A heads up or some honest help would be friendly,
Thanks.

 

[nocturnal]

What happens when you take the transpose of the product of two matrices. That is, what is (AB)^t ?

 

[Benny]

(AB)^T = (B^T)(A^T)

(A^T)^-1 = (A^-1)^T...you can switch the transpose and inverse.

Then (A^T)(A^T)^-1 = ...

Note: You should check those identities, I can't remember if they are correct.