PLEASE EXPLAIN CLEARLY HOW TO SET UP TRANSITION MATRIX

A store sells three different brands of granola. Brand A accounts for $20\%$ of sales, Brand B for $50\%,$ and Brand C for $30\%.$ The store decides to offer weekly discount coupons for Brands A and C$,$ expecting for $25\%$ Brand B buyers to switch to Brand A$,10\%$ of Brand B buyers to switch to Brand C$,10\%$ of Brand $C$ buyers to switch to Brand A$,$ and $5\%$ of Brand A buyers to switch to Brand B$.$

a$.$ Write the transition matrix T corresponding to this information, and the matrix $M_0$ corresponding to the starting state of the customers.

b$.$ What is the percent of sales for each brand after $2$ weeks?

c$.$ What is the percent of sales for Brand B after $4$ weeks?

d$.$ What is the steady state in this situation?