  We establish the uniqueness and the asymptotic stability of the invariant
measure for the two dimensional Navier Stokes equations driven by a
multiplicative noise which is either bounded or with a sublinear or a linear
growth. We work on an effectively elliptic setting, that is we require that the
range of the covariance operator contains the unstable directions. We exploit
the generalized asymptotic coupling techniques of Glatt
Holtz,Mattingly,Richards(2017) and Kulik,Scheutzow(2018), used by these authors
for the stochastic Navier Stokes equations with additive noise. Here we show
how these methods are flexible enough to deal with multiplicative noise as
well. A crucial role in our argument is played by the Foias Prodi estimate in
expected valued, which has a different form (exponential or polynomial decay)
according to the growth condition of the multiplicative noise.
