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Question
If A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`, then verify (BA)T = ATBT
Solution
A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`
∴ AT = `[(2, 0, 1),(1, 3, -1)]` and BT = `[(0, 1),(3, -7),(5, 2)]`
BA = `[(0, 3, 5),(1, -7, 2)][(2, 1),(0, 3),(1, -1)]`
= `[(0 + 0 + 5, 0 + 9 - 5),(2 - 0 + 2, 1 - 21 - 2)]`
∴ BA = `[(5, 4),(4, -22)]` .....(i)
∴ ATBT = `[(2, 0, 1),(1, 3, -1)][(0, 1),(3, -7),(5, 2)]`
= `[(0 + 0 + 5, 2 - 0 + 2),(0 + 9 - 5, 1 -21 - 2)]`
= `[(5, 4),(4, -22)]` .....(ii)
From (i) and (ii), we get
(BA)T = ATBT
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