answer with explanation

Q. Let, { X, } be a Time Homogenous Markov chain with the transition probability matrix, P for the states 0 , 1, 2 and 3 is given by, 0.2 0.5 0.3 0 0.1 0.3 0.6 0 P = 0 0.4 0.3 0.3 0 0 0.5 0.5 a. Find P(2), P(4) , and P(16) , what is noticeable about P(16)? (3.0 Marks) b. Determine A() for n = 1, 2, ..., 1Gjiven the initial condition A() = [0, 0, 0, 1] From, A() _ A(n-1) P(3.0 Marks)