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Let $\alpha$ and $\beta$ be the roots of the equation $x^2 + x + 1 = 0$. Then for $y \neq 0$ in $\mathbb{R}$, $\begin{vmatrix} y + 1 & \alpha & \beta \ \alpha & y + \beta & 1 \ \beta & 1 & y + \alpha \end{vmatrix}$ is equal to:
(1) $y(y^2 - 1)$
(2) $y(y^2 - 3)$
(3) $y^3$
(4) $y^3 - 1$
BETA
