if $\displaystyle \begin{vmatrix}
a & b &c \\
d & e &f \\
g&h &k
\end{vmatrix}$=2
then
$\displaystyle \begin{vmatrix}
f & k-4c &2k+f \\
d & g-4a &2g+d \\
e&h-4b &2h+e
\end{vmatrix}$=-16
is it true?
Remember that determinant is a multilineal functions, so:
$\displaystyle \begin{vmatrix}f & k-4c &2k+f \\ d & g-4a &2g+d \\ e&h-4b &2h+e \end{vmatrix}=\begin{vmatrix}f & k &2k \\ d & g &2g \\ e&h &2h \end{vmatrix}+\begin{vmatrix}f & k &f \\ d & g &d \\ e&h &e \end{vmatrix}+$$\displaystyle \begin{vmatrix}f & -4c &2k \\ d & -4a &2g \\ e&-4b &2h \end{vmatrix}+\begin{vmatrix}f & -4c &f \\ d & -4a &d \\ e&-4b &e \end{vmatrix}$ ,
So....??
Tonio