Answer
$\det (B)=-32$
Work Step by Step
We have $A=\begin{bmatrix}
a & b & c\\
d & e &f\\
g & h & i
\end{bmatrix}$ and $\det (A)=4$
Multiplying the first row of $A$ by $3-4$, we obtain:
$A_1=\begin{bmatrix}
-4a & -4b & -4c\\
d & e &f\\
g & h & i
\end{bmatrix}$
$\det (A_1)=-4 \det (A)=-16$
Multiplying the second row of $A_1$ by $2$, we obtain:
$A_2=\begin{bmatrix}
-4a & -4b & -4c\\
2d & 2e &2f\\
g & h & i
\end{bmatrix}$
$\det (A_2)=2.\det (A_1)=-32$
Permutting the second and third rows of $A_2$ we obtain:
$A_3=\begin{bmatrix}
-4a & -4b & -4c\\
g & h & i\\
2d & 2e &2f
\end{bmatrix}$
$\det (A_3)=-\det (A_2)=32$
Permutting the first and second rows of $A_3$ we obtain:
$B=\begin{bmatrix}
g & h & i\\
-4a & -4b & -4c\\
2d & 2e &2f
\end{bmatrix}$
$\det (B)=-\det (A_3)=-32$
