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In this paper, we derive the optimal structure of the source precoding matrices and the relay amplifying matrix for a two-way amplify-and-forward multiple-input multiple-output (MIMO) relay communication system where linear minimal mean-squared error (MMSE) receivers are used at both destinations. We show that for a broad class of frequently used objective functions for MIMO communications, the optimal relay and source matrices have a general beamforming structure. Based on this optimal structure, a new iterative algorithm is developed to optimize the relay and source matrices. The performance of the proposed algorithm is demonstrated by numerical simulations.