Let $\alpha $ and $\beta $ be the roots of the equation x2 + x + 1 = 0. Then for y $ \ne $ 0 in R, $$$\left| {\matrix{ {y + 1} & \alpha & \beta \cr \alpha & {y + \beta } & 1 \cr \beta & 1 & {y + \alpha } \cr } } \right|$$$ is equal to

Question

Let $\alpha $ and $\beta $ be the roots of the equation x² + x + 1 = 0. Then for y $ \ne $ 0 in R,
$$$\left| {\matrix{ {y + 1} & \alpha & \beta \cr \alpha & {y + \beta } & 1 \cr \beta & 1 & {y + \alpha } \cr } } \right|$$$ is equal to

y(y² – 1)