Question

The determinant $\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2}–bc & b^{2}–ca & c^{2}–ab \end{matrix} \right|$ is equal to -

• A. 0
• B. 1
• C. –1
• D. None

Answer 1

Answer: (A)

0

Answer 2

∆ = $\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} \right|$ – $\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ bc & ca & ab \end{matrix} \right|$

=$\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} \right|$ – $\frac{1}{abc}$ $\left| \begin{matrix} a & b & c \\ a^{2} & b^{2} & c^{2} \\ abc & bca & cab \end{matrix} \right|$

=$\left| \begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{matrix} \right|$–$\left| \begin{matrix} a & b & c \\ a^{2} & b^{2} & c^{2} \\ 1 & 1 & 1 \end{matrix} \right|$ = 0