Going to work on a few more problems before I take a look at Random Walks, Martingales, and Markov chains together as they share some things in common as presented in the book.
Let be a Markov chain with values in and a function. Will the sequence form a Markov chain? Will the reversed sequence form a Markov chain?
For the first part, the answer is yes because
The reversed sequence will also form a Markov chain