Using properties of determinants prove that: \[ \left|\begin{array}...

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Using properties of determinants prove that:
\[
\left|\begin{array}{lll}
b^{2} c^{2} & b c & b+c \\
c^{2} a^{2} & c a & c+a \\
a^{2} b^{2} & a b & a+b
\end{array}\right|=0 .
\]
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