Proof of Theorem NMLIC

This is a proof where we can chain together equivalences, rather than proving the two halves separately.

\begin{align*} \text{$A$ nonsingular}&\iff\text{$\homosystem{A}$ has a unique solution}&&\knowl{./knowls/definition.NM.knowl}{\text{Definition NM}}\\ &\iff\text{columns of $A$ are linearly independent}&&\knowl{./knowls/theorem.LIVHS.knowl}{\text{Theorem LIVHS}}\\ \end{align*}