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If \( 1, \omega \) and \( \omega^{2} \) are the cube roots of unity and
\( \mathrm{P} \)
\[
\left[\begin{array}{cc}
1+\omega & 2 \omega \\
-2 \omega & -b
\end{array}\right]+\left[\begin{array}{cc}
\mathrm{a} & -\omega \\
3 \omega & 2
\end{array}\right]=\left[\begin{array}{cc}
0 & \omega \\
\omega & 1
\end{array}\right]
\]
W
then \( a^{2}+b^{2} \) is equal to:
(A) \( 1+\omega^{2} \)
(B) \( \omega^{2}-1 \)
(C) \( 1+\omega \)
(D) \( (1+\omega)^{2} \)
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