Final answer:
The determinant of a rank one matrix is always zero unless it's a special case of a zero vector. The determinant of an odd-ordered skew-symmetric matrix is always zero, while an even-ordered skew-symmetric matrix can have a non-zero determinant.
Step-by-step explanation:
To find the determinants of a rank one matrix and a skew-symmetric matrix, it's important to understand the properties of these matrices.
A rank one matrix can be written in the form uvT, where u and v are column vectors. The determinant of such a matrix is always zero, unless one of the vectors is a zero vector, which is a special case.
A skew-symmetric matrix has the property that AT = -A. For a skew-symmetric matrix of odd order, the determinant is always zero. Meanwhile, a skew-symmetric matrix of even order can have a non-zero determinant, which can be found using standard determinant-finding techniques such as expansion by minors or using properties of determinants.