The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k² has no solution if k equals.

The value of the determinant $$\left| {\matrix{ {1 - \alpha } & {\alpha - {\alpha ^2}} & {{\alpha ^2}} \cr {1 - \beta } & {\beta - {\beta ^2}} & {{\beta ^2}} \cr {1 - \gamma } & {\gamma - {\gamma ^2}} & {{\gamma ^2}} \cr } } \right|$$ is equal to

If p + q + r = a + b + c = 0, then the determinant $$\left| {\matrix{ {pa} & {qb} & {rc} \cr {qc} & {ra} & {pb} \cr {rb} & {pc} & {qa} \cr } } \right|$$ equals

If $$A = \left[ {\matrix{ \alpha & 2 \cr 2 & \alpha \cr } } \right]$$ and det (A³) = 125, then $$\alpha$$ is equal to