The value of the determinant

Given: $\Delta=\left|\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x\end{array}\right|$

$\Delta=\left|\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x\end{array}\right|$

Taking $(3 x)$ common from $R_{3}$

$\Rightarrow \Delta=(3 x)\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 1 & 2 & 3\end{array}\right|$

$\Rightarrow \Delta=(3 x)(0)$         ( $\because$ The value of determinant with two identicals rows is equal to zero)

$\Rightarrow \Delta=0$

Hence, the value of the determinant $\Delta=\left|\begin{array}{ccc}1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 x & 6 x & 9 x\end{array}\right|$ is $\underline{0}$.