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The IKKT model is proposed as a non-perturbative formulation of superstringtheory. We propose a Dirac operator on the noncommutative torus,which isconsistent with the IKKT model, based on noncommutative geometry. Next, weconsider zero-mode equations of the Dirac operator with magnetic fluxes. Wefind that zero-mode solutions have the chirality and the generation structuressimilar to the commutative case. Moreover, we compute Yukawa couplings ofchiral matter fields.

Matrix model and Yukawa couplings on the noncommutative torus