determinants

• How to Calculate a Determinant by First-Row Cofactor Expansion
  Expand along the first row by multiplying each entry by its signed minor. See the alternating signs, a worked 3×3 example, and common errors.
• How to Find the Determinant of a Skew-Symmetric Matrix
  A skew-symmetric matrix has determinant zero when its order is odd; for even order, use its Pfaffian. See the 4 × 4 formula and example.