Transposing and Inversing Matrices

[bronxbombas]

Homework Statement

Prove that if A is an invertible matrix, then A*A^T and A^T*A are also invertible.

Homework Equations

(A^T)^-1=(A^-1)^T
(AB)^T=A^TB^T

The Attempt at a Solution

I just can't wrap my brain around this one. I know that I have to multiply a matrix by its inverse to get the identity matrix, but I don't know where to go from there.

 

[Dick]

(AB)^T=B^T*A^T. Not A^T*B^T. Now that we've gotten past that, what would be the inverse of A*A^T given both of the elements in the product have inverses?