Question

If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.

विकल्प

• `1/5[(1, 3),(2, -1)]`

• `1/5[(3, 1),(2, 1)]`

• `1/5[(-3, 2),(4, -1)]`

• `1/5[(3, -1),(-2, 1)]`

Answer 1

If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to `1/5[(3, 1),(2, 1)]`.

Explanation:

A = `[(1, -1),(2, 3)]`

AX = I

⇒ A^–1AX = A^–1I

⇒ X = A^–1

|A| = 5

∴ A^–1 = `1/5[(3, 1),(-2, 1)]`