for a 3 x 3 matric of values a11 a12 a13 b21 b22 b23 c31 c32 c33 the determinant will be a11a22a33+a12a23a31+a13a21a32-a13a22a31-a12a21a33-a11a23a32 the last three are negative because they are odd permutations. The first three are even permutations A permutation apparently is found by the number that are out of order, order being 1,2,3,4 increasing. 4,2,1,3 would result in a 2+1=3 permutation I believe. How does all of this fit together? I do not understand why permutations matter in relation to the determinant, which fits into the inverse and so on.