  We investigate one of the simplest multi-species generalizations of the one
dimensional exclusion process with reflective boundaries. The Markov matrix
governing the dynamics of the system splits into blocks (sectors) specified by
the number of particles of each kind. We find matrices connecting the blocks in
a matrix product form. The procedure (generalized matrix ansatz) to verify that
a matrix intertwines blocks of the Markov matrix was introduced in the periodic
boundary condition, which starts with a local relation [Arita et al, J. Phys. A
44, 335004 (2011)]. The solution to this relation for the reflective boundary
condition is much simpler than that for the periodic boundary condition.
