Let A be a 3 × 3 skew-symmetric matrix with integer entries. If |A| = k, then which of the following is true?
Correct: A
For any skew-symmetric matrix of odd order, the determinant is always zero. This is because for a skew-symmetric matrix A, A^T = -A. Taking determinant: |A^T| = |-A| => |A| = (-1)^n |A|. For n = 3 (odd), (-1)^3 = -1, so |A| = -|A|, which implies 2|A| = 0, hence |A| = 0. Therefore k = 0. This is a fundamental property: the determinant of a skew-symmetric matrix of odd order is always zero.