If $A$ is $m\times n$, then $Y$ is $n\times m$. The equation $AY=I_m$ makes every standard basis <vector> of $\mathbb R^m$ a linear combination of the columns of $A$: take the corresponding column of $Y$ as coefficients. Hence the <column space> is all of $\mathbb R^m$, giving \b[$\operatorname{rank}(A)=m$]. In particular, $n\ge m$ and $A$ has <full row rank>.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 4 / c / i / Solution

 Solution (source code)