1. The problem statement, all variables and given/known data Suppose A is a square matrix of size n. When is det(-A) = -det(A)? 2. Relevant equations N/A 3. The attempt at a solution My approach to the problem is to simply multiply the size n identity matrix by -1, then multiplied by A. For example: det((-1)*IdentityMatrix[n]*A) = det((-1)*IdentityMatrix[n])*det(A). At this point I could answer the original question by saying this is true when n is odd. But I get the impression I am overlooking some other very obvious answer or condition, and am wondering if anyone can think of a different approach. Thanks.