Question

If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)

Answer 1

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)