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Question
For the matrices A and B, verify that (AB)′ = B'A' where `A =[(0), (1),(2)] , B =[1 , 5, 7]`
Solution
Given, `"A" = [(0), (1),(2)] , "and B" = [(1 , 5, 7)]`
So, Ab = `[(0), (1),(2)] xx [(1 , 5, 7)]`
`= [(0 xx 1, 0 xx 5, 0 xx 7),(1 xx 1, 1 xx 5, 1 xx 7),(2 xx 1, 2 xx 5, 2 xx 7)]`
`= [(0,0,0), (1, 5,7),(2, 10,14)]`
Now, (AB)' = `[(0,1,2),(0,5,10),(0,7,14)]` ...(i)
So, A' = `[(0,1,2)]` and B' = `[(1),(5),(7)]`
Now, B'A' = `[(1),(5),(7)] xx [(0,1,2)]`
`= [(1 xx 0, 1 xx 1, 1 xx 2), (5 xx 0, 5 xx 1, 5 xx 2), (7 xx 0, 7 xx 1, 7 xx 2)]`
`= [(0,1,2),(0,5,10),(0,7,14)]` ...(ii)
Equations (i) and (ii) prove that,
∴(AB)' = B'A'
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