For an n x n matrix A, what is the relationship between det(A) and det(-A)? I tried it with a 1x1 matrix, and det (-A) = - det (A) I tried it with a 2x2 matrix, and det(A) = det(-A) I tried it with a 3x3 matrix, and the results were the same as that with a 1x1. This leads me to believe that for all odd n's, det(-A) = - det(A) and that for all even n's the two are the same. Is this the case? And if so, how would I show that in a more mathematical manner that just intuition?