Question

Given A = `[(1, 1),(8, 3)]` evaluate A² − 4A.

Answer 1

A = `[(1, 1),(8, 3)]`

A² = A x A = `[(1, 1),(8, 3)][(1, 1),(8, 3)]`

= `[(1 xx 1 + 1 xx 8, 1 xx 1 + 1 xx 3),(8 xx 1 + 3 xx 8, 8 xx 1 + 3 xx 3)]`

= `[(1 + 8, 1 + 3),(8 + 24, 8 + 9)]`

= `[(9, 4),(32, 17)]`

4A = `4[(1, 1),(8, 3)]`

= `[(4, 4),(32, 12)]`

A² − 4A = `[(9, 4),(32, 17)] - [(4, 4),(32, 12)]`

= `[(9 - 4, 4 - 4),(32 - 32, 17 - 12)]`

= `[(5, 0),(0, 5)]`