If A is an n x n skew-symmetric real matrix and n is odd, the determinant of A is strictly:

(A) 0

(B) 1

(C) -1

(D) n

Answer Key:

A

### Solution: For skew-symmetric matrix, A^T = -A. det(A^T) = det(-A) = (-1)^n det(A). If n is odd, det(A) = -det(A) ==> 2 det(A) = 0 ==> det(A) = 0. Correct: A.

← Prev Question Next Question →