An ݑŸ-potent matrix in ݑ0ݑ›(R) is an ݑ› × satisfying ݐذݑŸ = ݐ¸. A multiplicative semigroup S said to be decomposable if there exists a special kind of common invariant subspace called standard for each ݐ´ ∈ S. semi-group non-negative matrices known rank (ݑ†) > ݑŸ − 1 all ݑ† Further, nonnegative will full has no zero row and column. We have studied the structure maximal semi-groups under conditi...