  To describe the representation theory of the quantum Weyl algebra at an $l$th
primitive root $\gamma$ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley
found all nonsingular irreducible matrix solutions to the equation $yx-\gamma
xy=1$, assuming $yx\neq xy$. In this note, we complete their result by finding
and classifying, up to equivalence, all irreducible matrix solutions $(X, Y)$,
where $X$ is singular.
