Possible tests of neutrino maximal mixing and comments on matter effects

We show in a simple and general way that matter effects do not contribute to the averaged value of the probabilities of transition of solar $\nu_e$'s into other states in the case of maximal mixing of any number of massive neutrinos. We also show that future solar neutrino experiments (Super-Kamiokande and SNO) will allow to test the model with maximal mixing of three massive neutrinos in a way that does not depend on the initial solar neutrino flux.