A) \[abc\]
B) \[1/abc\]
C) \[ab+bc+ca\]
D) 0
Correct Answer: D
Solution :
\[\left| \,\begin{matrix} 1/a & {{a}^{2}} & bc \\ 1/b & {{b}^{2}} & ca \\ 1/c & {{c}^{2}} & ab \\ \end{matrix}\, \right|\]\[=\frac{1}{abc}\,\left| \,\begin{matrix} 1 & {{a}^{3}} & abc \\ 1 & {{b}^{3}} & abc \\ 1 & {{c}^{3}} & abc \\ \end{matrix}\, \right|=\frac{abc}{abc}\left| \,\begin{matrix} 1 & {{a}^{3}} & 1 \\ 1 & {{b}^{3}} & 1 \\ 1 & {{c}^{3}} & 1 \\ \end{matrix}\, \right|=0\]
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