Question

If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A^-1 = ______

पर्याय

• A

• A²

• A³

• A⁴

Answer 1

If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A^-1 = A³

Explanation:

`|A| = |(3, -3, 4), (2, -3, 4), (0, -1, 1)| = 1 ≠ 0`

adj A = `[(1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`

∴ `A^-1 = [(1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`

`A^2 = [(3, -4, 4), (0, -1, 0), (-2, 2, -3)]`

`A^3 = A^2. A = [(1, -1, 0), (-2, 3, -4), (-2, 3, -3)] = A^-1`