Given an nxn matrix A with mutually orthonormal columns, how does one show that A has mutually orthonormal rows WITHOUT assuming that A is orthogonal (A^T = A^-1)? I can show that A has mutually orthogonal rows by using the orthogonality between the row space and null space of a matrix, as well as the fact that the columns of A span R^n, but I need to show that the rows also have unit length. That is where I am getting stuck.
A similar question was asked here: Orthonormal columns and rows ; however, in trying to prove that A is orthogonal iff A has orthonormal columns, they don't show that AA^T = I given orthonormal columns, so their proof seems incomplete (if A is orthogonal, then A^T *A = I AND AA^T = I). To finish the proof, I believe they would need to answer my question.