Using properties of determinants prove that: \( \mathrm{P} \) \[ \l...

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Using properties of determinants prove that:
\( \mathrm{P} \)
\[
\left|\begin{array}{ccc}
a & a+2 b & a+2 b+3 c \\
3 a & 4 a+6 b & 5 a+7 b+9 c \\
6 a & 9 a+12 b & 11 a+15 b+18 c
\end{array}\right|=-a^{3} .
\]
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