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Question
If A = `[(2, -1),(3, -2),(4, 1)]` and B = `[(0, 3, -4),(2, -1, 1)]`, verify that (BA)T = AT BT
Solution
BA = `[(0, 3, -4),(2, -1, 1)] [(2, -1),(3, -2),(4, 1)]`
= `[(0 + 9 - 16, 0 - 6 - 4),(4 - 3 + 4, -2 + 2 + 1)]`
∴ BA = `[(-7, -10),(5, 1)]`
∴ (BA)T = `[(-7, 5),(-10, 1)]` ...(i)
ATBT = `[(2, 3, 4),(-1, -2, 1)] [(0, 2),(3, -1),(-4, 1)]`
= `[(0 + 9 - 16, 4 - 3 + 4),(0 - 6 - 4, -2 + 2 + 1)]`
= `[(-7, 5),(-10, 1)]` ...(ii)
From (i) and (ii), we get
(BA)T = ATBT
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