  We show that a suitable rescaling of the matrix model coupling constant makes
manifest the duality group of the N=2 SYM theory with gauge group SU(2). This
is done by first identifying the possible modifications of the SYM moduli
preserving the monodromy group. Then we show that in matrix models there is a
simple rescaling of the pair $(S_D,S)$ which makes them dual variables with
$\Gamma(2)$ monodromy. We then show that, thanks to a crucial scaling property
of the free energy derived perturbatively by Dijkgraaf, Gukov, Kazakov and
Vafa, this redefinition corresponds to a rescaling of the free energy which in
turn fixes the rescaling of the coupling constant. Next, we show that in terms
of the rescaled free energy one obtains a nonperturbative relation which is the
matrix model counterpart of the relation between the $u$--modulus and the
prepotential of N=2 SYM. This suggests considering a dual formulation of the
matrix model in which the expansion of the prepotential in the strong coupling
region, whose QFT derivation is still unknown, should follow from perturbation
theory. The investigation concerns the SU(2) gauge group and can be generalized
to higher rank groups.
