Prove that if A is nonsingular then (A^T)^-1 = (A^-1)^T

[mpm]

I am having to do a proof on a problem and am not really seeing it for some reason. Maybe it's because I have been doing the homework for so long.

Prove that if A is nonsingular then A^T is nonsingular and

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

Hint: (AB)^T = B^T*A^T

I understand the hint, but I can't seem to get an image of the actual problem.

Can anyone help me?

 

[quasar987]

Start from $(A^{-1}A)^T=I$.