Originally Posted by

**arbolis** Ah ok, how strange. There are at least 3 types of basic operations on rows which are in fact the same as to multiply an elemental matrix by the original matrix. But I didn't know that one of them (and problably another one too. The one that multiply a row by a scalar) would have an effect on the determinant... Thanks so much for the info.

So if I understood well, when I have to reduce a matrix into a triangular one, I better use the operation "multiply a row by a scalar and add it to another row" and not the other two ones so that the determinant is not changed.