[SOLVED] Triangular matrix/determinant

The problem says "Reduce the following matrix into an upper triangular one in order to find its determinant".

I wonder why they ask me to reduce it since the calculus would only get more complicated.

So here is the matrix I call it . I reduced it to this one : I call it . I calculate the determinant of which is . By curiosity I calculated the one from and surprisingly I got ... So my guess is that I made an error when I reducted into . Am I right saying this? Because I think the determinant of and must be the same, right?

Last question : why do they wanted me to reduce ? It's much more simple to directly calculate without passing by a reduction of matrix and then calculating .