Determine the value of a second determinant based on the first I know the theory of determinants, but I have no idea how to apply it to this problem.
Suppose $$\det\begin{bmatrix}a&b&c\\ d&e&f\\ g&h&i \end{bmatrix} = 6$$
What is the value of
$$\det\begin{bmatrix}g - 2a&h - 2b&i - 2c\\ 3a&3b&3c\\2d&2e&2f \end{bmatrix}$$
The options for the answers are:


*

*4

*36

*24

*-24


$$\det\begin{bmatrix}g - 2a&h - 2b&i - 2c\\ 3a&3b&3c\\2d&2e&2f \end{bmatrix}$$
$$=\det\begin{bmatrix}g&h&i\\ 3a&3b&3c\\2d&2e&2f \end{bmatrix}$$ (Applying $R_1'=R_1+\frac23 R_2$)
$$=3\cdot2\cdot \det\begin{bmatrix}g&h&i\\ a&b&c\\d&e&f \end{bmatrix}$$ (Taking out $3,2$ as common factors from the $R_2,R_3$ respectively)
$$=(-1)3\cdot2\cdot \det\begin{bmatrix}a&b&c\\ g&h&i\\d&e&f \end{bmatrix}$$ (Exchanging $R_1,R_2$ resulting '-' sign )
$$=(-1)(-1)3\cdot2\cdot \det\begin{bmatrix}a&b&c\\d&e&f\\ g&h&i \end{bmatrix}$$
(Exchanging $R_2,R_3$ resulting '-' sign  again)
