How to prove that an orthonormal matrix inverse's is its transpose?

Question

I saw a definition of an orthonormal matrix that says: "A squared matrix is orthonormal if its columns are orthonormal" And from this definition, it says that A^-1=A^T. Now. I understand that A's columns are independent and because it is a square matrix it's also invertible. And I also understand that A^T * A = I. But to show that A^-1 = A^T we need to show that A * A^T = I also and I don't know how to prove it. Thanks!