Complete solution please

There are three types of grocery stores in a given community. Within this community there always exists a shift of customers from one grocery store to another. On January 1, % shopped at store 1, 1/3 at store 2 and 5/12 at store 3. Each month store 1 retains 90% of its customers and loses 10% of them to store 2. Store 2 retains 5% of its customers and loses 85% of them to store 1 and 10% of them to store 3. Store 3 retains 40% of its customers and loses 50% to store 1 and 10% to store 2. a) Find the transition matrix b) What proportion of customers will each store retain by April 1 and June 1. c) Assuming the same pattern continues, what will be the long-run distribution (equilibrium) of customers among the three stores? d) Prove that an equilibrium has actually been reach in part (c)