Question 127
Determine all triples $(a, b, c)$ of real numbers satisfying the system of equations
$$
\begin{aligned}
& a^{2}+a b+c=0 \\
& b^{2}+b c+a=0 \\
& c^{2}+c a+b=0
\end{aligned}
$$
$$
\begin{aligned}
& a^{2}+a b+c=0 \\
& b^{2}+b c+a=0 \\
& c^{2}+c a+b=0
\end{aligned}
$$