Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 3 / 9H / a

States $i,j\in S$ communicate when each is accessible from the other: there exist nonnegative integers $m,n$ such that $P^m(i,j)>0$ and $P^n(j,i)>0$. A communicating class is an equivalence class for this relation.