Question

If the inverse of the matrix A = `[(1, 1, -1), (1, -2, 1), (2, -1, -3)]` is `1/9 [(7, 4, -1), (5, -1, -2), (3, 3, a)]`, then a is equal to ______ 

Options

• 4

• -3

• 2

• -2

Answer 1

If the inverse of the matrix A = `[(1, 1, -1), (1, -2, 1), (2, -1, -3)]` is `1/9 [(7, 4, -1), (5, -1, -2), (3, 3, a)]`, then a is equal to -3.

Explanation:

AA^-1 = I

`1/9 [(1, 1, -1), (1, -2, 1), (2, -1, -3)] [(7, 4, -1), (5, -1, -2), (3, 3, a)] = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

⇒ `[(1, 0, (-3 - a)/9), (0, 1, (3 + a)/9), (0, 0, (-a)/3)] = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

∴ By equality of matrices, we get

`(3 + a)/9 = 0 ⇒ a = -3`