I need help specially with item a . I can see this is true but I don't know how to show it mathematically.

Matrices are far too useful to remain the exclusive property of physicists. They may appear wherever there are linear relations. For instance, in a study of population move- ment the initial fraction of a fixed population in each of n areas (or industries or religions, etc.) is represented by an n-component column vector P. The movement of people from one area to another in a given time is described by an n x n (stochastic) matrix T. Here Tij is the fraction of the population in the jth area that moves to the ith area. (Those not moving are covered by i = j.) With P describing the initial population distribution, the final population distribution is given by the matrix equation TP = Q From its definition, _ _Pi = 1. (a) Show that conservation of people requires that Cnij = 1, j= 1, 2,.... n. i=1 (b) Prove that n Cei = 1 i=1 continues the conservation of people