Without expanding the determinant, prove that: \[ \left|\begin{array}{ccc} 1 & a & b c \\ 1 & b ...

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Without expanding the determinant, prove that:
\[
\left|\begin{array}{ccc}
1 & a & b c \\
1 & b & c a \\
1 & c & a b
\end{array}\right|=\left|\begin{array}{ccc}
1 & a & a^{2} \\
1 & b & b^{2} \\
1 & c & c^{2}
\end{array}\right|
\]
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