Question:
Write the value of the determinant $\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$
Solution:
$\left|\begin{array}{ccc}2 & 3 & 4 \\ 5 & 6 & 8 \\ 6 x & 9 x & 12 x\end{array}\right|$
$=\left|\begin{array}{lll}2 & 3 & 4 \\ 5 & 6 & 8 \\ 2 & 3 & 4\end{array}\right|$ [Taking $2 x$ common from $R_{3}$ ]
$=0$ $\left[\because R_{1}\right.$ and $R_{3}$ are identical $]$