Can orthonormal columns lead to orthonormal rows in a square matrix?

[td21]

"orthonormal columns imply orthonormal rows for square matrix."

My proof is:
Q^{T}Q=I(orthonormal columns)
implys
QQ^{T}=I(orthonoraml rows)

for square matrix.


But i think this proof is kind of indirect. Is there another more direct proof from the definition of inner product or norm?

 

[Fredrik]

I think that's as direct and simple as it gets. I would only add the explanation of how Q^TQ=I implies QQ^T=I.