It follows from Theorem 4.2 that for a time reversible Markov chain It turns out that if

Question:

It follows from Theorem 4.2 that for a time reversible Markov chain

It turns out that if the state space is finite and Pij > 0 for all i, j , then the preceding is also a sufficient condition for time reversibility. (That is, in this case, we need only check Eq. (4.26) for paths from i to i that have only two intermediate states.) Prove this.
Hint: Fix i and show that the equations