Question

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

• A. 1
• B. 0
• C. 2
• D. 3

Answer 1

Answer: (B)

Operating $R_1\to R_1-R_2$
$R_2\to R_2-R_3$
$\left|\begin{array}{ccc}0& a-b& (a-b)(a+b+c)\\ 0& b-c& (b-c)(a+b+c)\\ 1& c& c^2-ab\end{array}\right|$
$\Rightarrow (a-b)(b-c)\left|\begin{array}{ccc}0& 1& a+b+c\\ 0& 1& a+b+c\\ 1& c& c^2-ab\end{array}\right|=0$
Because $R_1$ and $R_2$ are identical.
Hence (b) is the correct answer.