If $f(x)=\begin{vmatrix}0 & x-a& x-b\\x+a& 0 & x-c\\x+b & x+c& 0\end{vmatrix}$, then f(0) is :

0

The correct answer is Option (4) → 0

$f(x)=\begin{vmatrix}0 & x-a& x-b\\x+a& 0 & x-c\\x+b & x+c& 0\end{vmatrix}⇒f(0)=\begin{vmatrix}0 & -a& -b\\a& 0 & -c\\b & c& 0\end{vmatrix}$

as it is skew symmetric

$A=-A^T$

so $|A|=-|A^T|$

so $|A|=0$

so $f(0)=0$