1. The problem statement, all variables and given/known data Let A and B be n x n matrices. Show that if AB = -BA and n is odd, then A or B is singular. 2. Relevant equations - A matrix is singular iff its determinant is 0. or possibly: Theorem: if A and B are both n x n matrices, then |AB| = |A||B| 3. The attempt at a solution I kind of have a proof, but it doesn't seem correct. AB = -BA therefore |A||B| = -(|B||A|) 2|A||B| = 0 |A||B| = 0 therefore |A| = 0 or |B| = 0 thus, A or B is singular. This doesn't make use of the fact that n is odd, as specified, which is why I don't think it's correct.