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In this letter, we provide an expression of spatial multiplexing gain (SMG) for two mutually interfering multiple-input multiple-output (MIMO) broadcast channels, referred to as MIMO-IBC, with linear transceiver. We derive the SMG with respect to user antenna distribution, and compare the systems with and without cooperation among receive antennas in each cell. Additionally, we propose a linear precoding and decoding algorithm for the MIMO-IBC which maximizes the sum rate by extending a solution for single-cell multiple-input single-output broadcast channels. Simulation results confirm the accuracy of our theoretical SMG analysis for the MIMO-IBC.