Question

If A = `[(1, 2),(4, 1)]`, find A² + 2A + 7I.

Answer 1

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

∴ A² = A · A

= `[(1,  2),(4, 1)] [(1, 2),(4, 1)]`

= `[(1 + 8, 2 + 2),(4 + 4, 8 + 1)]`

= `[(9, 4),(8, 9)]`

∴ A² + 2A + 7I = `[(9, 4),(8, 9)] + [(2, 4),(8, 2)] + [(7, 0),(0, 7)]`

= `[(18, 8),(16, 18)]`