Question

If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A⁻¹ B⁻¹)

Answer 1

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

∴ A = `[(2, 4),(1, 3)]`

A = (2 × 3) - (4 × 1)

A = 6 - 4

A = 2

∴ B = `[(1, 1),(0, 1)]`

B = (1 × 1) - (1 × 0)

B = 1 - 0

B = 1

(A⁻¹ B⁻¹) = `1/|"A"| ("adj A") * 1/|"B"|  ("adj B")`

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

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

`= 1/2 [(3, -7),(-1, 3)]`