Binary operations are in general more difficult to implement when compared with unary operations. Normally any operation on a graph involves vertices or edges or both together. In general two graphs are involved in binary operation. Hajos construction is one such operation which involves vertices and edges with three operations. So two graphs with three operations on vertices and edges increases the difficulty in implanting it. Computation time increases when this operation is to be verified for all possible edge pairs between the two graphs. A matrix representation for this purpose would enable easy computation. In this paper we have provided a matrix method of verifying if two graphs are Hajos stable. © Published under licence by IOP Publishing Ltd.