The distributivity numbers of $\mathcal{P}(\omega )$/fin and its square

We show that in a model obtained by forcing with a countable support iteration of Mathias forcing of length $\omega _{2}$, the distributivity number of ${\mathcal{P}}(\omega )$/fin is $\omega _{2}$, whereas the distributivity number of r.o.$({\mathcal{P}}(\omega )$/fin)$^{2}$ is $\omega _{1}$. This answers a problem of Balcar, Pelant and Simon, and others.