Question

The value of the determinant$\left| \begin{matrix} a–b & b–c & c–a \\ x–y & y–z & z - x \\ p–q & q–r & r–p \end{matrix} \right|$ is –

• A. 0
• B. abc + pqr + xyz
• C. (a – x)(y – z)(r – p)
• D. None of these

Answer 1

Answer: (A)

0

Answer 2

C₁ → C₁ + C₂ + C₃

∆ = $\left| \mspace{6mu}\begin{matrix} 0 & b - c & c - a \\ 0 & y - z & z - x \\ 0 & q - r & r - p \end{matrix}\mspace{6mu} \right|$ = 0