Question

If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B^–1 A^–1)^–1 is equal to ______.

Options

• `[(2, -2),(2, 3)]`

• `[(2, 2),(-2, 3)]`

• `[(2, -3),(2, 2)]`

• `[(1, -1),(-2, 3)]`

Answer 1

If A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`, then (B^–1 A^–1)^–1 is equal to `underlinebb([(2, -2),(2, 3)]`.

Explanation:

It is given that A = `[(2, 2),(-3, 2)]`, B = `[(0, -1),(1, 0)]`

As, (B^–1 A^–1)^–1 = (A^–1)^–1 (B^–1)^–1  ...[∵ (A^–1)^–1 = A^–1]

= AB     ...[∵ (AB)^–1 = B^–1 A^–1]

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

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

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