Show that if (left(X_{n} ight)) is a Markov chain with finite state space (E) such that (i

Show that if \(\left(X_{n}\right)\) is a Markov chain with finite state space \(E\) such that \(i \longrightarrow j\) for all states \(i\) and \(j\), and such that there exists a state \(i_{0}\) with \(T\left(i_{0}, i_{0}\right)>0\), then the chain is regular (i.e., it has a regular transition diagram, in the sense of Chapter 1 ).