Using properties of determinants, prove \[ \left|\begin{array}{ccc} 1 & 1+p & 1+p+q \\ 2 & 3+2 p...

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Using properties of determinants, prove
\[
\left|\begin{array}{ccc}
1 & 1+p & 1+p+q \\
2 & 3+2 p & 4+3 p+2 q \\
3 & 6+3 p & 10+6 p+3 q
\end{array}\right|=1
\]
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