Question

If A = `[(2, 2),(4, 5)]` and A^–1 = λ(adj(A)), then λ = ______ .

विकल्प

• `(-1)/2`

• `1/3`

• `(-1)/3`

• `1/2`

Answer 1

If A = `[(2, 2),(4, 5)]` and A^–1 = λ(adj(A)), then λ = `1/2`.

Explanation:

`|"A"| = |(2, 2),(4, 5)|` = 2 ≠ 0

A^–1 = `1/|"A"|` adjA

= λ(adj A)   ......[Given]

∴ λ = `1/|"A"| = 1/2`