Linear Algebra

For any skew-symmetric matrix $A^T = -A$: $\det(A) = \det(A^T) = \det(-A) = (-1)^n \det(A)$ For $n = 3$ (odd order): $\det(A) = -\det(A) \implies 2\det(A) = 0 \implies \det(A) = 0$