How many multiplication required to calculate matrix product, Mathematics

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(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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