Suppose that two urns A and B contain a total of N balls. Assume that at time t, there are exactly k balls in A. At time t + 1, a ball and an urn are chosen with probability depending on the contents of the urn (i.e., a ball is chosen from A with probability k/N or from B with probability (N - k)/N). Then, the ball is placed into one of the urns, where urn A is chosen with probability k/N or urn B is chosen with probability (N - k)/N. Determine the transition matrix of the Markov chain with states represented by the contents of A.