Question

If inverse of matrix `[(7, -3, -3),(-1, 1, 0),(-1, 0, 1)]` is the matrix `[(1, 3, 3),(1, lambda, 3),(1, 3, 4)]`, then value of λ is ______.

Options

• −4

• 1

• 3

• 4

Answer 1

If inverse of matrix `[(7, -3, -3),(-1, 1, 0),(-1, 0, 1)]` is the matrix `[(1, 3, 3),(1, lambda, 3),(1, 3, 4)]`, then value of λ is 4.

Explanation:

Given, A = `[(7, -3, -3),(-1, 1, 0),(-1, 0, 1)]` and A⁻¹ = `[(1, 3, 3),(1, lambda, 3),(1, 3, 4)]`

Since, AA⁻¹ = I

∴ `[(7, -3, -3),(-1, 1, 0),(-1, 0, 1)] [(1, 3, 3),(1, lambda, 3),(1, 3, 4)] = [(1, 0, 0),(0, 1, 0),(0, 0, 0)]`

`[(1, 12-3lambda, 0),(0, -3+lambda, 0),(0, 0, 1)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

On comparing matrices, we get 

12 − 3λ = 0 and −3 + λ = 1

⇒ λ = 4 and λ = 4