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Question
If A = `[(1, 4),(1, 0)], "B" = [(2, 1),(3, -1)] and "C" = [(2, 3),(0, 5)]` compute (AB)C = (CB)A ?
Solution
Given
A = `[(1, 4),(1, 0)]`
B = `[(2, 1),(3, -1)]`
C = `[(2, 3),(0, 5)]`
(AB) C = `[[(1, 4),(1, 0)] xx [(2, 1),(3, -1)]][(2, 3),(0, 5)]`
= `[(2 + 12, 1 - 14),(2 + 0, 1 + 0)][(2, 3),(0, 5)]`
= `[(14, -13),(2, 1)][(2, 3),(0, 5)]`
= `[(28 + 0, 42 - 15),(4 + 0, 6 + 5)]`
= `[(28, 27),(4, 11)]`
(CB) A = `[[(2, 3),(0, 5)][(2, 1),(3, -1)]][(1, 4),(1, 0)]`
= `[(4 + 9, 2 - 3),(0 + 15, 0 - 5)][(1, 4),(1, 0)]`
= `[(13, 1),(15, 5)][(1, 4),(1, 0)]`
= `[(13 - 1, 52 + 0),(15 - 5, 60 + 0)]`
= `[(12, 52),(10, 60)]`
It is clear from above that
(AB) C ≠ )CB) A.
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