A taxicab driver moves between the airport A and two hotels Band C according to the following rules. If he is at the airport, he will go to one of the two hotels next with equal probability. If at a hotel then he returns to the airport with probability 3/4 and goes to the other hotel with probability 1/4.

(a) Find the transition matrix for the chain.

(b) Suppose the driver begins at the airport at time 0.

Find the probability for each of his three possible locations at time 2 and the probability that he is at hotel B at time 3.