On this mini-course we will learn how to extend the MPA formulation to the multispecies case with the very simple SSEP dynamics. Due to the jump symmetries of each particle in the bulk, this formulation allows us to compute any phisical quantity without resorting to the matrices representation. Nevertheless, their existence is still a necessary condition for the formulation to work. We will give an example of such matrices and focus on the exploitation of the induced algebra.