Question

If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B⁻¹ A⁻¹)⁻¹.

Answer 1

(B⁻¹ A⁻¹)⁻¹ = [(AB)⁻¹]⁻¹     .......[∵ (AB⁻¹) = B⁻¹ A⁻¹]

= AB

∴ (B⁻¹ A⁻¹)⁻¹ = `[(2, 2),(-3, 2)] [(0, -1),(1, 0)]`

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

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