Question

If a 3 × 3 matrix A has its inverse equal to A, then A² = ______ 

विकल्प

• `[(0, 1, 1), (0, 1, 0), (1, 0, 1)]`

• `[(1, 1, 1), (1, 1, 1), (1, 0, 1)]`

• `[(1, 0, 1), (0, 1, 0), (0, 0, 0)]`

• `[(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

Answer 1

If a 3 × 3 matrix A has its inverse equal to A, then A² = `underline([(1, 0, 0), (0, 1, 0), (0, 0, 1)]`

Explanation:

`A^-1 = A`

⇒ `A^-1 A = A. A`

⇒ `A^2 = I = [(1, 0, 0), (0, 1, 0), (0, 0, 1)]`