(a) Show that the product of two 2 2 stochasticmatrices is also a stochastic matrix.(b)

Chapter 3, Problem 3.7.14

(choose chapter or problem)

(a) Show that the product of two 2 2 stochasticmatrices is also a stochastic matrix.(b) Prove that the product of two n n stochasticmatrices is also a stochastic matrix.(c) If a 2 2 stochastic matrix P is invertible, prove thatP1 is also a stochastic matrix.Suppose we want to know the average (or expected) numberof steps it will take to go from state i to state j in a Markovchain. It can be shown that the following computationanswers this question: Delete the jth row and the jth columnof the transition matrix P to get a new matrix Q. (Keepthe rows and columns of Q labeled as they were in P.) Theexpected number of steps from state i to state j is given bythe sum of the entries in the column of (I Q)1 labeled i.15.