  Under the assumption that the approximating function $\psi$ is monotonic, the
classical Khintchine-Groshev theorem provides an elegant probabilistic
criterion for the Lebesgue measure of the set of $\psi$-approximable matrices
in $\R^{mn}$. The famous Duffin-Schaeffer counterexample shows that the
monotonicity assumption on $\psi$ is absolutely necessary when $m=n=1$. On the
other hand, it is known that monotonicity is not necessary when $n > 2$
(Sprindzuk) or when $n=1$ and $m>1$ (Gallagher). Surprisingly, when $n=2$ the
situation is unresolved. We deal with this remaining case and thereby remove
all unnecessary conditions from the classical Khintchine-Groshev theorem. This
settles a multi-dimensional analogue of Catlin's Conjecture.
