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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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