Question

The value of determinant $\left|\begin{array}{ccc}a-b& b-c& c-a\\ b-c& c-a& a-b\\ c-a& a-b& b-c\end{array}\right|$ is equal to

• A. abc
• B. 2abc
• C. 0
• D. 4abc

Answer 1

The correct option is C 0

The value of the determinant $\left|\begin{array}{ccc}a-b& b-c& c-a\\ b-c& c-a& a-b\\ c-a& a-b& b-c\end{array}\right|$
Applying $C_1\to C_1+C_2+C_3$
$\Rightarrow \left|\begin{array}{ccc}0& b-c& c-a\\ 0& c-a& a-b\\ 0& a-b& b-c\end{array}\right|=0$
Hence, option C.