In 1983 Dan Voiculescu used a family of unitary matrices, now
known as "Voiculescu's Unitaries," to provide the first counter-example to
an old conjecture of Halmos regarding "almost commuting" matrices. Later,
Ruy Exel and Terrry Loring used "Voiculescu's Unitaries" in an elementary
and elegant proof to provide another counter-example on "almost commuting"
matrices. In this talk, we present two new counter-examples using
"Voiculescu's Unitaries." The talk should be accessible to anyone with
knowledge of basic real analysis and linear algebra.