Question

Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C

Answer 1

We have,

A = `[(1, 2),(-1, 3)]`

B = `[(4, 0),(1, 5)]`

C = `[(2, 0),(1, -2)]`

And a = 4, b = –2

(BC) = `[(4, 0),(1, 5)] [(2, 0),(1, -2)]`

= `[(8, 0),(7, -10)]`

And A(BC) = `[(1, 2),(-1, 3)] [(8, 0),(7, -10)]`

= `[(8 + 14,0 - 20),(-8 ++21, 0 - 30)]`

= `[(22, -20),(13,-30)]`

Also, AB = `[(1, 2),(-1, 3)] * [(4, 0),(1, 5)]`

= `[(4 + 2, 0 + 10),(-4 + 3, 0 +15)]`

= `[(6, 10),(-1, 15)]`

∴ (AB)C = `[(6, 10),(-1, 15)] [(2, 0),(1, -2)]`

= `[(22, -20),(13, -30)]`

= A(BC)

Hence proved.