| , * 20 c 1/a & a^2 & bc 1/b & b^2 & ca 1/c & c^2 & ab , | = - Vidyadip

Question

$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right| = $

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Answer

d
(d)$\left| {\,\begin{array}{*{20}{c}}{1/a}&{{a^2}}&{bc}\\{1/b}&{{b^2}}&{ca}\\{1/c}&{{c^2}}&{ab}\end{array}\,} \right|$$ = \frac{1}{{abc}}\,\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&{abc}\\1&{{b^3}}&{abc}\\1&{{c^3}}&{abc}\end{array}\,} \right| = \frac{{abc}}{{abc}}\left| {\,\begin{array}{*{20}{c}}1&{{a^3}}&1\\1&{{b^3}}&1\\1&{{c^3}}&1\end{array}\,} \right| = 0$

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