Explanation

(d)
Given that, $\left| \begin{matrix}
\frac{1}{a} & a^{2} & bc \\
\frac{1}{b} & b^{2} & ca \\
\frac{1}{c} & c^{2} & ab
\end{matrix} \right| = \frac{1}{abc}\left| \begin{matrix}
1 & a^{3} & abc \\
1 & b^{3} & abc \\
1 & c^{3} & abc
\end{matrix} \right|$
$= \frac{abc}{abc}\left| \begin{matrix}
1 & a^{3} & 1 \\
1 & b^{3} & 1 \\
1 & c^{3} & 1
\end{matrix} \right|$
$= 0$
$(\because$ columns $C_{1}$ and $C_{3}$ are same)