If \( a, b \in \mathbf{R} \) and \[ \Delta=\left|\begin{array}{ccc}...

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If \( a, b \in \mathbf{R} \) and
\[
\Delta=\left|\begin{array}{ccc}
a & a+b i & b i \\
a+b i & b i & a \\
b i & a & a+b i
\end{array}\right|
\]
then \( \Delta \) equals
(a) \( a^{3}+b^{3} i \)
(b) \( 2\left(a^{3}+b^{3}\right) \)
(c) \( a^{3}-b^{3} i \)
(d) \( -2\left(a^{3}-b^{3} i\right) \)
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