If P is a skew-symmetric matrix of order 3, then what is \det(P) equal to?

Explanation

For any skew-symmetric matrix P, P^T = -P. Taking the determinant on both sides yields \det(P^T) = \det(-P). For an n \times n matrix, \det(-P) = (-1)^n \det(P). Since n = 3 (odd), we get \det(P) = -\det(P), which implies 2\det(P) = 0, so \det(P) = 0.

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