71. It follows from Theorem 4.2 that for a time reversible Markov chain Image It turns out that if the state space is finite andI mage for allI mage, 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 Image are satisfied byI mage, where c is chosen so thatI mage.