Consider a random walk among 3 points labelled {a,b, c}. Each minute, she makes a move, and her move

Consider a random walk among 3 points labelled {a,b, c}. Each minute, she makes a move, and her movements are dictated by the following constraints that follows:(i) If (current position) equals (previous-minute position), then go to any one of the other two positions with equal probability;(ii) If (current position) does not equal (previous-minute position), then continue to stay in current position during the next minute.Please answer the following questions:(a). Determine the state-space, such that the system evolution can be described by a Discrete Time Markov Chain. Justify your answer. Draw the state transition diagram, with the states labeled and the edges labeled with the transition probabilities.(b). Is the Markov chain irreducible and a periodic?