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We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed. Itdoi:10.1088/1751-8113/49/47/475001 fatcat:g4dyjzj5izejlizcnu2yejyxue