It is one of the property of skew symmetric matrix. If, we have any skew-symmetric matrix with odd order then we can directly write its determinant equal to zero. We can verify this property using an example of skew-symmetric 3x3 matrix. We can find its determinant using co-factors and can verify that its determinant is equal to zero.

To look at an example of skew matrix go through the file present below. I have showed that determinant of skew-symmetric matrix with odd order is equal to zero.