= Solution
In the column convention used for <QR factorization>, an $m\times k$ real matrix has <orthonormal columns> when $Q^TQ=I_k$. This says that each column has unit norm and distinct columns have zero <inner product>. If $Q$ is square, then $Q^TQ=I$ provides a left inverse; a square matrix with a left inverse is invertible, so \b[$Q^{-1}=Q^T$], and also $QQ^T=I$. Such a square matrix is an <orthogonal matrix>. A rectangular matrix with orthonormal columns generally has no two-sided inverse.
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