  Let $M(d,\chi)$ be the moduli space of semistable sheaves of rank 0, Euler
characteristic $\chi$ and first Chern class $dH (d>0)$, with $H$ the hyperplane
class in $\mathbb{P}^2$. We give a description of $M(d,\chi)$, viewing each
sheaf as a class of matrices with entries in
$\bigoplus_{i\geq0}H^0(\mathcal{O}_{\mathbb{P}^2}(i))$. We show that there is a
big open subset of $M(d,1)$ isomorphic to a projective bundle over an open
subset of a Hilbert scheme of points on $\mathbb{P}^2.$ Finally we compute the
classes of M(4,1), M(5,1) and M(5,2) in the Grothendieck group of varieties,
especially we conclude that M(5,1) and M(5,2) are of the same class.
