Question

If A = `[(1, -2),(2, 1)], B = [(3, 1),(-2, 2)]`, then (A + B) (A − B) is equal to ______.

Options

• `[(-12, -11),(12, -3)]`

• `[(12, -11),(12, -3)]`

• `[(-12, 11),(-12, -3)]`

• `[(-12, -11),(-12, -3)]`

Answer 1

If A = `[(1, -2),(2, 1)], B = [(3, 1),(-2, 2)]`, then (A + B) (A − B) is equal to `underlinebb([(-12, -11),(12, -3)])`.

Explanation:

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

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

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

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

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

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

(A + B) (A − B) = `[(4, -1),(0, 3)] xx [(-2, -3),(4, -1)]`

= `[(4 xx (-2) + (-1) xx 4, 4 xx -3 + (-1) xx (-1)),(0 xx (-2) + 3 xx 4,0 xx (-3) + 3 xx (-1))]`

= `[(-12, -11),(12, -3)]`