Suppose a car rental agency in large city has three locations: a downtown location (labeled A), an airport location (labeled B), and a hotel lecation (labeled C). The agency has a group of delivery drivers to serve all three locations. Of the calls to the downtown location, 30%are delivered in the downtown area, 30% are delivered to the airport, and 40% are delivered to the hotel. Of the calls to the airport location, 40% are delivered in the downtown area, 40% are delivered to the airport, and 20% are delivered to the hotel. Of the calls to the hotel location, 50% are delivered in the downtown area, 30% are delivered to the airport area, and 20% are delivered to the hotel area. After making a delivery, a driver goes to the nearest location to make the next delivery. This way, the location of a specific driver is determined only by his or her previous location. (A) Give the transition matrix. (B) Find the probability that a driver who begins in the downtown location will be at the hotel after two deliveries. (C) In the long run, what fraction of the total number of stops does a driver make at each of the three locations?