Solution
= Solution
\b[Yes.] The three nontrivial <detailed balance> identities are
$$
\pi_AP_{AB}=\frac18=\pi_BP_{BA},
$$
$$
\pi_AP_{AC}=\frac18=\pi_CP_{CA},
$$
and
$$
\pi_BP_{BC}=\frac1{24}=\pi_CP_{CB}.
$$
\b[Thus the chain is a <reversible Markov chain>.]