If ω is a complex cube root of unity and A = ω 0 0 0 ω 2 0 0 0 1 then A - 1 = …

Step-by-step solution

Given, ω is a complex cube root of unity ∴ ω 3 = 1 Given matrix A can be written as A = l A ⇒ ω 0 0 0 ω 2 0 0 0 1 = 1 0 0 0 1 0 0 0 1 A On apply R 1 → ω 2 R 1 , R 2 → ω R 2 , we get ⇒ ω 3 0 0 0 ω 3 0 0 0 1 = ω 2 0 0 0 ω 0 0 0 1 A ⇒ 1 0 0 0 1 0 0 0 1 = ω 2 0 0 0 ω 0 0 0 1 A A - 1 = ω 2 0 0 0 ω 0 0 0 1