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Question
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
Solution
AB = `[(2,3),(1,-6)] [(-1,4),(1,-2)]`
`= [(-2+3,8-6),(-1-6,4+12)] = [(1,2),(-7,16)]`
adj(AB) = `[(16,-2),(7,1)]` ....(1)
B = `[(-1,4),(1,-2)]` ∴ adj B = `[(-2,-4),(-1,-1)]`
A = `[(2,3),(1,-6)]` ∴ adj A = `[(-6,-3),(-1,2)]`
∴ (adj B)(adj A) = `[(-2,-4),(-1,-1)] [(-6,-3),(-1,2)]`
`= [(12 + 4, 6 - 8),(6 + 1, 3-2)]`
`= [(16,-2),(7,1)]` .....(2)
From (1) and (2),
adj (AB) = (adj B) (adj A)
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