  Let $\Gamma$ be a non-commutative free group on finitely many generators. In
a previous work two of the authors have constructed the class of multiplicative
representations of $\Gamma$ and proved them irreducible as representation of
$\Gamma\ltimes_\lambda C(\Omega)$. In this paper we analyze multiplicative
representations as representations of $\Gamma$ and we prove a criterium for
irreducibility based on the growth of their matrix coefficients.
