Question

If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A^-1 is ______ 

विकल्प

• A^T

• A²

• A

• I

Answer 1

If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A^-1 is A^T.

Explanation:

|A| = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)] = -1 ≠ 0`

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

∴ `A^-1 = 1/|A|`(adj A)

= `[(0, 1, 0), (-1, 0, 0), (0, 0, -1)] = A^T`