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Question
Given the matrices:
A = `[(2, 1),(4, 2)]`, B = `[(3, 4),(-1, -2)]` and C = `[(-3, 1),(0, -2)]`. Find:
- ABC
- ACB.
State whether ABC = ACB.
Solution
i. AB = `[(2, 1),(4, 2)][(3, 4),(-1, -2)]`
= `[(6 - 1, 8 - 2),(12 - 2, 16 - 4)]`
= `[(5, 6),(10, 12)]`
ABC = `[(5, 6),(10, 12)][(-3, 1),(0, -2)]`
= `[(-15 + 0, 5 - 12),(-30 + 0, 10 - 24)]`
= `[(-15, -7),(-30, -14)]`
ii. AC = `[(2, 1),(4, 2)][(-3, 1),(0, -2)]`
= `[(-6 + 0, 2 -2),(-12 + 0, 4 - 4)]`
= `[(-6, 0),(-12, 0)]`
ACB = `[(-6, 0),(-12, 0)][(3, 4), (-1, -2)]`
= `[(-18 - 0, -24 - 0),(-36 - 0, -48 - 0)]`
= `[(-18, -24),(-36, -48)]`
Hence, ABC = ACB.
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