matrices - Determinant of $ 3times 3$ matrix by using gauss

I am trying to calculate the determinant of the following matrix by performing Gaussian elimination. I know that the determinant is $1$ but I get the wrong result.

\begin{bmatrix}
1 & 1 & 1 \\

1 & 1 & 0 \\
2 & 3 & -4
\end{bmatrix}

$r_2-r_1$ gives:

\begin{bmatrix}
1 & 1 & 1 \\
0 & 0 & -1 \\
2 & 3 & -4

\end{bmatrix}

$r_3-2r_1$ gives:

\begin{bmatrix}
1 & 1 & 1 \\
0 & 0 & -1 \\
0 & 1 & -6
\end{bmatrix}

Swap $r_2$ and $r_3$

\begin{bmatrix}
1 & 1 & 1 \\
0 & 1 & -6 \\
0 & 0 & -1
\end{bmatrix}

Determinant$= 1.1.(-1) = -1$ which is wrong.

Answer

As you swap rows $r_2$ and $r_3$, you introduce a negative one in the determinant, hence the determinent is $-(-1)=1$.