Question

If $f(x)=\left|\begin{array}{ccc}{x}^3-x& a+x& b+x\\ x-a& x^2-x& c+x\\ x-b& x-c& 0\end{array}\right|$ then

• A. f(1)=0
• B. f(2)=0
• C. f(0)=0
• D. f(-1)=0

Answer 1

Answer: (C)

$f(0)=\left|\begin{array}{ccc}0& a& b\\ -a& 0& c\\ -b& -c& 0\end{array}\right|$
$f(0)$ is the determinant of skew-symmetric matrix of order $3$ (odd).
$\therefore f(0)=0.$