How many multiplication required to calculate matrix product, Mathematics

(a) Assume that A is a m1×m2 matrix and B is a m2×m3 matrix. How many multiplications are required to calculate the matrix product AB?

(b) Given that A1 is a 20 × 50 matrix, A2 is a 50 × 10 matrix and A3 is a 10 × 40 matrix. What are the dimensions of the matrix product A1A2A3? What is the most effcient way (least number of multiplications) to calculate the matrix product A1A2A3? (A1A2)A3 or A1(A2A3)? Give a reason for your answer.

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