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Evaluate |1/a a^2 bc||1/b b^2 ca||1/c c^2 ab|

Let ∆ = |\begin{matrix} 1 / a & a^{2} & bc \\ 1 / b & b^{2} & ca \\ 1 / c & c^{2} & ab \end{matrix}| = \frac{1}{abc} |\begin{matrix} 1 & a^{3} & abc \\ 1 & b^{3} & abc \\ 1 & c^{3} & abc \end{matrix}| = \frac{abc}{abc} |\begin{matrix} 1 & a^{3} & 1 \\ 1 & b^{3} & 1 \\ 1 & c^{3} & 1 \end{matrix}| = 0 [as, C_{1} and C_{3} are identical]

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