Question

Given martices A = `[(2, 1),(4, 2)] and "B" = [(3, 4),(-1, -2)], "C" = [(-3, 1),(0, -2)]` Find the products of (i) ABC (ii) ACB and state whether they are equal.

Answer 1

A = `[(2, 1),(4, 2)]`

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

C = `[(-3, 1),(0, -2)]`

ABC = `[(2, 1),(4, 2)] xx [(3, 4),(-1, -2)] xx [(-3, 1),(0, -2)]`

= `[(6 - 1, 8 - 2),(12 - 2, 16 - 4)][(-3, 1),(0, -2)]`

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

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

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

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

= `[(-6 + 0, 2 - 2),(-12 + 10, 4 - 4)] xx [(3, 4),(-1, -2)]`

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

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

= `[(-18, -24),(-36, -48)]`
∴ ABC ≠ ACB.