Question

Solve the following :

if A = `[(1, 2),(-1, 3)]`, then find A³.

Answer 1

A² = A · A = `[(1, 2),(-1, 3)][(1, 2),(-1, 3)]`

= `[(1 - 2, 2 + 6),(-1 - 3, -2 + 9)]`

∴ A² = `[(-1, 8),(-4, 7)]`

∴ A³ = A² · A = `[(-1, 8),(-4, 7)][(1, 2),(-1, 3)]`

= `[(-1 - 8, -2 + 24),(-4 - 7, -8 + 21)]`

∴ A³ = `[(-9, 22),(-11, 13)]`.