Let A be a 3×2 matrix and B a 2×5 matrix. A third matrix D is of order 3×5.
(i) Decide whether the product AB is defined. Give a clear reason and state the order of AB.
(ii) Examine whether the product BA is defined. Explain your answer, quoting the necessary condition on orders.
(iii) If C is a 5×4 matrix, comment on the possibility of adding the matrices AB and C. Justify your conclusion.
(iv) When the matrix D replaces C, the sum AB+D is defined. Find the total number of elements contained in AB+D.