I have one doubt. If EA = U where E is elimination matrix and U is upper tringular , then det(EA) = det(E)*det(A) = det(U). However at property 7 it was discussed that we first carry out elimination , get U and then use property 7 since it is easier that way and determinant of U will be same as A. That's only possible if det(E) = 1 (by using property 9). Is that always the case?####[]