If \( p \) and \( q \) are distinct primes, and \[ \Delta=\left|\be...

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If \( p \) and \( q \) are distinct primes, and
\[
\Delta=\left|\begin{array}{ccc}
\sqrt{p q} & p i & q+\sqrt{p q} i \\
p \sqrt{q} & \sqrt{p}+p \sqrt{p} i & q \sqrt{p}+\sqrt{p} q i \\
q \sqrt{p} & \sqrt{p}+p \sqrt{q} i & q \sqrt{q}+q \sqrt{q} i
\end{array}\right|
\]
then \( \Delta \) is
(a) an integer
(b) irrational
(c) non-zero rational
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