3. (Tucker 3.3.12) The Markov chain expression pit1 = Api, can be inverted as, Pi-1 = A 'pi, so long as A is non-singular; this suggests a Markov chain that moves backwards in time. Consider the following Markov transition matrices: 50 0 .25 0 (2) .5 1 5 (2i) .5 .5 .5 OT 0 .25 (a) Find the inverse of each matrix, or classify it as singular. (b) For the non-singular matrices, find pi-1 if pi = [.5, 0, .5]T. (c) Are the inverted processes actually Markov chains? Explain your