Answer
0
Work Step by Step
$\left| \begin{matrix}
1 & 1 & 1 \\
2 & 2 & 2 \\
-3 & 4 & -5 \\
\end{matrix} \right|$
Include the 2 common from ${{R}_{2}}$.
The determinant will be as here
$2\left| \begin{matrix}
1 & 1 & 1 \\
1 & 1 & 1 \\
-3 & 4 & -5 \\
\end{matrix} \right|$
Here, ${{R}_{1}}$ and ${{R}_{2}}$ are similar.
Therefore, $\left| \begin{matrix}
1 & 1 & 1 \\
2 & 2 & 2 \\
-3 & 4 & -5 \\
\end{matrix} \right|=0$
