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We propose a general method to find exact ground state solutions to theSU($N$) invariant matrix model arising from the quantization of the11-dimensional supermembrane action in the light-cone gauge. We illustrate themethod by applying it to lower dimensional models and for the SU(2) group. Thisapproach can be used to find ground state solutions to the complete9-dimensional model and for any SU($N$) group. The supercharges and theconstraints related to the SU(2) symmetry are the relevant operators and theygenerate a multicomponent wave function. In the procedure, the fermionicdegrees of freedom are represented by means of Dirac-like gamma matrices. Weexhibit a relation between these finite $N$ matrix theory ground statesolutions and SUSY quantum cosmology wave functions giving a possible physicalsignificance to the theory even for finite $N$

A general procedure to find ground state solutions for finite $N$ M(atrix) theory. Reduced models and SUSY quantum cosmology