Question

If adj(A) = `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`, find A^–1 

Answer 1

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

∴ |adj A| =  `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`

Expanding along R₁ –(– 2)[36 – 18]

= 2(18)

= 36

A^–1 = `+- 1/sqrt(|"adj A"|)`

adj A = `+- 1/sqrt(36) [(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`

= `+- 1/6 [(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`