plz explain step-by-step

A cop and a thief move independently back and forth between two rooms: The cop (at every time step) moves from the current room to the other room with probability 0.8 (and stays otherwise) Starting from Room 1, The thief moves to Room 2 with probability 0.3 (and stays otherwise). Starting from Room 2, the thief moves to room 1 with probability 0.6 (and stays otherwise) a) Find the transition matrices and stationary distributions of the Cop Chain and the Thief chain. b) There are 4 possible (cop, thief) states: both in Room 1, the cop in Room 1 and the thief in Room 2, the cop in Room 2 and the thief in Room 1, and both in Room 2. Call these states 1,2,3, and 4, and let Z, be the number representing the (Cop, thief) state in time n. Is Zo, Z1, Z2, .. A Markov Chain? Explain your answer. c) Now let us suppose that the cop will catch the thief if they are in the same room. Find the expected number of steps taken until the cop catches the thief under two initial scenarios: When the cop starts in Room 1 and the thief starts in Room 2, and vice versa. Hint: Call a and b the expected times for the two initial scenarios, respectively, and then condition on the first move of the cop and the first move of the thief