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


We switch the first and the second row and the second and third row so
$$\det\begin{bmatrix}g - 2a&h - 2b&i - 2c\\ 3a&3b&3c\\2d&2e&2f \end{bmatrix}=3\times 2\times \det\begin{bmatrix}a&b&c\\ d&e&f\\ g - 2a&h - 2b&i - 2c\end{bmatrix}$$
and we add $2\times$ the first row to the third row we find
$$\det\begin{bmatrix}g - 2a&h - 2b&i - 2c\\ 3a&3b&3c\\2d&2e&2f \end{bmatrix}=3\times 2\times \det\begin{bmatrix}a&b&c\\ d&e&f\\ g &h &i \end{bmatrix}=6\times 6=36$$
