JEE Math Practice Question
For a real number $\alpha$, if the system \[ \left[\begin{array}{ccc} 1 & \alpha & \alpha^{2} \\ \alpha & 1 & \alpha \\ \alpha^{2} & \alpha & 1 \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\left[\begin{array}{r} 1 \\ -1 \\ 1 \end{array}\right] \] of linear equations, has infinitely many solutions, then what is the value of $1+\alpha+\alpha^{2}$?
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