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Question
If A = `[(5, 2, 9),(1, 2, 8)]`, B = `[(1, 7),(1, 2),(5, -1)]` verify that (AB)T = BT AT
Solution
Given A = `[(5, 2, 9),(1, 2, 8)]`, B = `[(1, 7),(1, 2),(5, -1)]`
AB = `[(5, 2, 9),(1, 2, 8)] xx [(1, 7),(1, 2),(5, -1)]`
= `[(5 + 2 + 45, 35 + 4 - 9),(1 + 2 + 40, 7 + 4 - 8)]`
= `[(52, 30), (43, 3)]`
(AB)T = `[(52, 43), (30, 3)]` ...(1)
BT = `[(1, 1, 5),(7, 2, -1)]`
AT = `[(5, 1),(2, 2),(9, 8)]`
BT AT = `[(1, 1, 5),(7, 2, -1)] xx [(5, 1),(2, 2),(9, 8)]`
= `[(5 + 2 + 45, 1 + 2 + 40),(35 + 4 - 9, 7 + 4 - 8)]`
= `[(52, 43),(30, 3)]` ...(2)
From (1) and (2) we get, (AB)T = BT AT
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