linear algebra - Determinant of Triangular Matrix

I understand that you can find the determinant of a matrix along it's diagonal if it is in triangular form. For a matrix such as this:

$$\begin{pmatrix} 1 & 5 & 0\\ 2 & 4 & -1\\ 0 &-2 & 0 \end{pmatrix}$$
When put into triangular form I get:
$$\begin{pmatrix} 1 & 5 & 0\\ 0 & 1 & 1/6\\ 0 & 0 & 1/3 \end{pmatrix}$$

Since I multiplied row two by -1/6 during the row reduction I would expect the determinant to be
$$1\cdot 1\cdot 1/3\cdot (-1/6),$$
but the answer for the determinant of the original matrix is -2. Where exactly am I going wrong?