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Question
For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`
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Solution
Given, A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`
So, AB = `[(1),(-4),(3)] xx [(-1, 2, 1)]`
= `[(1 xx (-1), 1 xx 2, 1 xx 1), (-4 xx (-1), -4 xx 2, -4 xx 1),(3 xx (-1), 3 xx 2, 3 xx 1)]`
= `[(-1, 2, 1), (4, -8, -4), (-3, 6, 3)]`
Now, (AB)' = `[(-1, 4, -3),(2, -8, 6), (1, -4, 3)]` ...(i)
A' = `[(1, -4, 3)]` and B' = `[(-1),(2),(1)]`
Now, B'A' = `[(-1),(2),(1)] xx [(1, -4, 3)]`
= `[(-1 xx 1, -1 xx (-4), -1 xx 3),(2 xx 1, 2 xx (-4), 2 xx 3), (1 xx 1, 1 xx (-4), 1 xx 3)]`
= `[(-1, 4, -3),(2, -8, 6),(1, -4, 3)]` ...(ii)
It is proved from the equation and that, (AB)' = B'A'
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