Question

The determinant $\left|\begin{array}{ccc}{b}^2-ab& b-c& bc-ac\\ ab-a^2& a-b& b^2-ab\\ bc-ac& c-a& ab-a^2\end{array}\right|$ is used to

• A. 1
• B. -1
• C. 0
• D. none of these.

Answer 1

Answer: (C)

Operating $C_1\to C_1+(a-b)C_2-C_3$, we get
$\left|\begin{array}{ccc}{b}^2-ab& b-c& bc-ac\\ ab-a^2& a-b& b^2-ab\\ bc-ac& c-a& ab-a^2\end{array}\right|$
$=\left|\begin{array}{ccc}0& b-c& bc-ac\\ 0& a-b& b^2-ab\\ 0& c-a& ab-a^2\end{array}\right|=0$