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Question
If A = `[(4, 3, 1),(2, 3, -8),(1, 0, -4)]`, B = `[(2, 3, 4),(1, 9, 2),(-7, 1, -1)]` and C = `[(8, 3, 4),(1, -2, 3),(2, 4, -1)]` then verify that A + (B + C) = (A + B) + C
Solution
B + C = `[(2, 3, 4),(1, 9, 2),(-7, 1, -1)] + [(8, 3, 4),(1, -2, 3),(2, 4, -1)]`
= `[(10, 6, 8),(2, 7, 5),(-5, 5, -2)]`
A + (B + C) = `[(4, 3, 1),(2, 3, -8),(1, 0, -4)] + [(10, 6, 8),(2, 7, 5),(-5, 5, -2)]`
= `[(14, 9, 9),(4, 10, -3),(-4, 5, -6)]` ....(1)
(A + B) = `[(4, 3, 1),(2, 3, 8),(1, 0, 4)] + [(2, 3, 4),(1, 9, 2),(-7, 1, -1)]`
= `[(6, 6, 5),(3, 12, -6),(-6, 1, -5)]`
(A + B) + C = `[(6, 6, 5),(3, 12, -6),(-6, 1, -5)] + [(8, 3, 4),(1, -2, 3),(2, 4, -1)]`
= `[(14, 9, 9),(4, 10, -3),(-4, 5, -6)]` ....(2)
From (1) and (2) we get
A + (B + C) = (A + B) + C
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