(a) Assume that A is a m_{1}×m_{2} matrix and B is a m_{2}×m_{3} matrix. How many multiplications are required to calculate the matrix product AB?
(b) Given that A_{1} is a 20 × 50 matrix, A_{2} is a 50 × 10 matrix and A_{3} is a 10 × 40 matrix. What are the dimensions of the matrix product A_{1}A_{2}A_{3}? What is the most effcient way (least number of multiplications) to calculate the matrix product A_{1}A_{2}A_{3}? (A_{1}A_{2})A_{3} or A_{1}(A_{2}A_{3})? Give a reason for your answer.