What is the relation between the matrices a and b- conduct

Question

(a) Let A = (a_ij ) be an n × m matrix representing a two-player zero-sum game, where the row player is Ann and the column player is Bill.

Let B = (b_ji) be a new m × n matrix in which the row player is Bill and the column player is Ann. What is the relation between the matrices A and B?

(b) Conduct a similar transformation of the names of the players in the following matrix and write down the new matrix.