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Question:

If A is a skew-symmetric matrix of order 3, then prove that det(A) = 0

Solution:

A is skew-symmetric means AT = -A. Taking determinant both sides, Det(AT) = Det(-A) => Det(A) = (-1)3Det(A) => Det(A) = -Det(A) => 2Det(A) = 0 => Det(A) = 0. Only for odd order, the determinant of a skew-symmetric matrix is zero.