5. A matrix P is said to be stochastic if the entries of P are nonnegative, and the sum of each row is one. A matrix P is said to be doubly stochastic if P is stochastic and the sum of each column is one. (a) Suppose P1 and P2 are stochastic matrices of the same order. Consider P3 := AP1 + (1 - A)P2 for A E [0, 1]; and P4 = P1P2. Which matrix (or matrices), P3 or P4 is (or are) stochastic? (b) Suppose P1 and P2 are doubly stochastic matrices of the same order. Consider P3 := AP1 + (1 - X)P2 for A E [0, 1]; and P4 = P1P2. Which matrix (or matrices), P3 or P4 is (or are) doubly stochastic