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If \( w \) is a complex cube root of unity, show that
\[
\left(\left[\begin{array}{lll}
1 & w & w^{2} \\
w & w^{2} & 1 \\
w^{2} & 1 & w
\end{array}\right]+\left[\begin{array}{lll}
w & w^{2} & 1 \\
w^{2} & 1 & w \\
w & w^{2} & 1
\end{array}\right]\right)\left[\begin{array}{l}
1 \\
w \\
w^{2}
\end{array}\right]=\left[\begin{array}{l}
0 \\
0 \\
0
\end{array}\right]
\]
W
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