Question

If A = `[(3, 1),(-1, 2)]`, find A² − 5A.

Answer 1

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

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

= `[(9 - 1, 3 + 2),(-3 -2, -1 + 4)]`

= `[(8, 5),(-5, 3)]`

5A = 5 × `[(3, 1),(-1, 2)]`

= `[(15, 5),(-5, 10)]`

A² − 5A = `[(8, 5),(-5, 3)] - [(15, 5),(-5, 10)]`

= `[(8 - 15, 5 - 5),(-5 - (-5), 3 - 10)]`

= `[(-7, 0),(0, -7)]`