1. The problem statement, all variables and given/known data det(A) = det(AT) = det(−A) = (−1)^n*det(A). Hence det(A) = 0 when n is odd I understand all of this except for the last statement: =(-1)^n*det(A). Why is this? Does it have to do with the cofactor expansion, and the "checkerboard" (as my professor puts it) of signs? I'm just not quite sure why that has to be. A quick explanation would be more than adequate. Thank you very much for your time. I didn't think that my post fit the rest of the template so I deleted it.