Question

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

Answer 1

2B − A²

2B = `2 [(3, 2),(-2, 1)]`

= `[(6, 4),(-4, 2)]`

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

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

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

= `[(-3, 0),(0, -3)]`

2B − A² = `[(6, 4),(-4, 2)] - [(-3, 0),(0, -3)]`

= `[(6 - (-3), 4 - 0),(-4 - 0, 2 - (-3))]`

= `[(9, 4),(-4, 5)]`