Question

If A = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: (AB)C = A(BC)

Answer 1

We have, A = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`

AB = `[(1, 2),(-2, 1)] [(2, 3),(3, -4)]`

= `[(2 + 6, 3 - 8),(-4 + 3, -6 - 4)]`

= `[(8, -5),(-1, -10)]`

And (AB)C = `[(8, -5),(-1, -10)] [(1, 0),(-1, 0)]`

= `[(8 + 5, 0),(-1 + 10, 0)]`

= `[(13, 0),(9, 0)]`  .....(i)

Again, (BC) = `[(2, 3),(3, -4)] [(1, 0),(-1, 0)]`

= `[(2 - 3, 0),(3 + 4, 0)]`

= `[(-1, 0),(7, 0)]`

And A(BC) = `[(1, 2),(-2, 1)] [(-1, 0),(7, 0)]`

= `[(-1 + 14, 0),(2 + 7, 0)]`

= `[(13, 0),(9, 0)]`  ......(ii)

From (i) and (ii), we get

∴ (AB)C= A(BC)