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

td21
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"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?
 
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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.
 

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