Redo Problem 5.17 for AB′ in Problem 5.19, where B′ is the transpose of B:

Note from Problems 5.19 to 5.21 that AB ≠ BA ≠ AB′. This further reflects the fact that matrix multiplication is not commutative.

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B' = 8 6 4 1 72 The product AB' is defined: 2 x 2 = 2 x 3. AB' will be 2 x 3. 35 8 6 4 RIC RC2 RC3 AB' = = 92 1 7 2 R2C1 R2C2 R2C3 3(8) +5(1) 3(6)+5(7) 3(4)+5(2) 29 53 22 = = 9(8) + 2(1) 9(6) + 2(7) 9(4) + 2(2) 74 68 40