Answer
The sign of the determinant reverses.
Work Step by Step
The sign of the solution of the determinant reverses when we interchange the columns of a determinant.
Example:
$\begin{align}
& \left| \begin{matrix}
1 & 2 \\
3 & 4 \\
\end{matrix} \right|=1\cdot 4-2\cdot 3 \\
& \text{ = }4-6 \\
& =-2
\end{align}$
Interchanging the columns of the determinant, we get,
$\begin{align}
& \left| \begin{matrix}
2 & 1 \\
4 & 3 \\
\end{matrix} \right|=2\cdot 3-1\cdot 4 \\
& \text{ }=6-4 \\
& =2
\end{align}$
The sign of the determinant reverses.
