Need a lot of help here guys. I need to prove that for an nxn matrix A, if i interchange two rows to obtain B, then det=-detA I have proved my basis (below), but i'm stuck on the hard part, the induction (which i'm required to do). I understand the steps of induction, but i don't know how to do it for this case. What i have so far: Let A be an nxn matrix. Basis n=2 Then detA=a(11)a(22) - a(12)a(21) Now let B be the matrix obtained by interchanging rows 1 and 2 Then detB=a(21)a(12) - a(22)a(11) =-detA So true for an arbitary 2x2 matrix. (induction) Assume true for n=k For a kxk matrix...?????