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Question
Given martices A = `[(2, 1),(4, 2)] and "B" = [(3, 4),(-1, -2)], "C" = [(-3, 1),(0, -2)]` Find the products of (i) ABC (ii) ACB and state whether they are equal.
Solution
A = `[(2, 1),(4, 2)]`
B = `[(3, 4),(-1, -2)]`
C = `[(-3, 1),(0, -2)]`
ABC = `[(2, 1),(4, 2)] xx [(3, 4),(-1, -2)] xx [(-3, 1),(0, -2)]`
= `[(6 - 1, 8 - 2),(12 - 2, 16 - 4)][(-3, 1),(0, -2)]`
= `[(5, 6),(10, 12)] xx [(-3, 1),(0, -2)]`
= `[(-15 + 0, 5 - 12),(-30 + 0, 10 - 24)]`
= `[(-15, -7),(-30, -14)]`
ACB = `[(2, 1),(4, 2)][(-3, 1),(0, -2)] xx [(3, 4),(-1, -2)]`
= `[(-6 + 0, 2 - 2),(-12 + 10, 4 - 4)] xx [(3, 4),(-1, -2)]`
= `[(-6, 0),(-12, 0)] xx [(3, 4),(-1, -2)]`
= `[(-18 + 0, -24 + 0),(-36 + 0, -48 + 0)]`
= `[(-18, -24),(-36, -48)]`
∴ ABC ≠ ACB.
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