Boolean matrix multiplication ($C_{ij}={\bigvee }_k(A_{ik}\wedge B_{kj})$)

For Boolean matrices, replace numerical addition by logical disjunction and multiplication by logical conjunction. Applied to adjacency matrices, the product records a walk formed by following one segment represented by the first matrix and one represented by the second. For an adjacency matrix $A$ on $n\ge 1$ vertices, start from $I\vee A$. Repeated squaring then computes reflexive transitive closure once the exponent reaches $n-1$: the identity entries pad shorter walks, and every reachable pair has a simple path of length at most $n-1$.