Question

Given the matrices:

A = `[(2, 1),(4, 2)]`, B = `[(3, 4),(-1, -2)]` and C = `[(-3, 1),(0, -2)]`. Find: 

1. ABC
2. ACB.
   State whether ABC = ACB.

Given the matrices:

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

Find the products of (i) A(BC) (ii) (AC)B and state whether they are equal.

Answer 1

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

= `[(6 - 1, 8 - 2),(12 - 2, 16 - 4)]`

= `[(5, 6),(10, 12)]`

ABC = `[(5, 6),(10, 12)][(-3, 1),(0, -2)]`

= `[(-15 + 0, 5 - 12),(-30 + 0, 10 - 24)]`

= `[(-15, -7),(-30, -14)]`

ii. AC = `[(2, 1),(4, 2)][(-3, 1),(0, -2)]`

= `[(-6 + 0, 2 -2),(-12 + 0, 4 - 4)]`

= `[(-6, 0),(-12, 0)]`

ACB = `[(-6, 0),(-12, 0)][(3, 4), (-1, -2)]`

= `[(-18 - 0, -24 - 0),(-36 - 0, -48 - 0)]`

= `[(-18, -24),(-36, -48)]`

ABC = `[(-15, -7),(-30, -14)]`

ACB = `[(-18, -24),(-36, -48)]`

Hence, ABC ≠ ACB.