Matrix

Algebra Level 4

The system of linear equations

X+γYZ=0γXYZ=0X+YγZ=0\begin{aligned} X + \gamma Y - Z &=0 \\ \gamma X - Y - Z &=0 \\ X + Y - \gamma Z &=0 \end{aligned}

has a non-trivial solution for __________.\text{\_\_\_\_\_\_\_\_\_\_}.

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