The relationship matrix is generally aimed at the relationship between a set and itself. If R is a relation on set A, then the relation matrix is a 3×3 matrix.

For the intersection operation ∩ reflexivity, symmetry and transitivity are preserved, while r∩q is still reflexive, symmetric and transitive, so s (r ∩ q) = t (r ∩ q) = r ∩ q.