Let A = [[0, 0, -1], [0, -1, 0], [-1, 0, 0]] (3x3 matrix with rows (0,0,-1), (0,-1,0), (-1,0,0)). The only correct statement about the matrix A is
- A. A is a zero matrix
- B. A^2 = I
- C. A^-1 does not exist
- D. A = (-1)I, where I is a unit matrix
Answer: B. A^2 = I
Explanation: Multiplying the 3×3 matrix A by itself: row 1 gives [0, 0, 1], row 2 gives [0, 1, 0], row 3 gives [1, 0, 0]. Hence A² = I (A is an involutory matrix).