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