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This paper considers a Gaussian two-user multiple-input multiple-output (MIMO) multiple access channel (MAC) with cooperating encoders. After defining a form of cooperation strategy, we derive achievable rate bounds by applying the results obtained by Willems for the MAC with generalised feedback. Then, we characterise an achievable rate region and also provide a lower bound for this region, which are very close. Although the achievable rate bounds are described by non-concave functions, the boundary of the achievable rate region could be generated by maximising a weighted sum of the rates. Numerical results obtained generally exceed the capacity region of a MIMO MAC without cooperation. Copyrigh