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?