The value of the determinant \(\begin{vmatrix} a - b & b - c & c - a \\ b - c & c - a & a - b \\ c - a & a - b & b - c \end{vmatrix}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
In every row the three elements add up to zero:
\((a - b) + (b - c) + (c - a) = 0\)
Applying \(C_1 \rightarrow C_1 + C_2 + C_3\) (which does not change the value of the determinant), the first column becomes all zeros:
\( \displaystyle \begin{vmatrix} 0 & b - c & c - a \\ 0 & c - a & a - b \\ 0 & a - b & b - c \end{vmatrix} \)
A determinant with a column of zeros has the value 0.