The Ordered Ra-Semigroup of Rectangular Matrices

In this paper, we consider the set of all m × n matrices over the real field R, denoted by Mm×n(R) and define the binary matrix operation ′⊗′ on Mm×n(R). It is shown that the set with the binary operation attains the structure of an RA-semigroup. Further the compatibility of natural partial order is verified with respect to this binary operation