Question

If A = `[(2, 3),(4, 5)]`, show that A² – 7A – 2I = 0

Answer 1

A = `[(2, 3),(4, 5)]`

∴ A² – 7A – 2I

= `[(2, 3),(4, 5)][(2, 3),(4, 5)] - 7[(2, 3),(4, 5)] - 2[(1, 0),(0, 1)]`

= `[(4 + 12, 6 + 15),(8 + 20, 12 + 25)] - [(14, 21),(28, 35)] - [(2, 0),(0, 2)]`

= `[(16 - 14 - 2, 21 - 21),(28 - 28, 37 - 35 - 2)]`

= `[(0, 0),(0, 0)]`

= 0