I don't even know where to start with this:
Let A be an n x n invertible matrix. Prove that A^{T} is invertible and determine its inverse in terms of A^{-1.}
Any hints or suggestions would be appreciated!
We know $\displaystyle A$ is invertible, and so $\displaystyle A^{-1}A=I$
Taking the transpose of both sides gives $\displaystyle A^T(A^{-1})^T=I$
What can you then conclude about the invertibility of $\displaystyle A^T?$