Suppose $EA=R$ with $E$ invertible, $R=\operatorname{RREF}(A)$, and rank $r$. Rows of $E$ express the corresponding rows of $R$ as combinations of the original rows. The bottom $m-r$ rows $z_i$ satisfy $z_iA=0$ and are independent, so their transposes form a basis of $\ker A^T$.
Over $\mathbb C$, their conjugate transposes form a basis of $\ker A^*$ for Hermitian left-null-space geometry. Row and column orientations must be stated.
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