i have a question from a mid session exam. I was marked incorrect and I dont understand why. Question: Given a reversible markov chain P, with measure $\pi$. Show that $P^2$ is reversible.
Since P is reversible $\pi$ is the invariant measure. Since $\pi$ is the invariant measure $\pi P = \pi$. Therefore, $\pi P^2=\pi PP =\pi P$. Which is reversible given from the question.