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Question: If a = \(\left| \begin{matrix} a–b & b–c & c–a \\ b–c & c–a & a–b \\ c–a & a–b & b–c \end{matrix} \r...

If a = ∣a–bb–cc–ab–cc–aa–bc–aa–bb–c∣\left| \begin{matrix} a–b & b–c & c–a \\ b–c & c–a & a–b \\ c–a & a–b & b–c \end{matrix} \right|, then

A

a = – 1

B

a = 1

C

a = 0

D

None of these

Answer

a = 0

Explanation

Solution

C1 ® C1 + C2 + C3

a = ∣0b–cc–a0c–aa–b0a–bb–c∣\left| \begin{matrix} 0 & b–c & c–a \\ 0 & c–a & a–b \\ 0 & a–b & b–c \end{matrix} \right| Ž a = 0