$$\left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]\left[ {\matrix{ 1 & \alpha \cr { - \alpha } & \beta \cr } } \right] = \left[ {\matrix{ {1 + {\alpha ^2}} & {\alpha - \alpha \beta } \cr {\alpha - \alpha \beta } & {{\alpha ^2} + {\beta ^2}} \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]$$

1 + $$\alpha$$² = 1

$$\alpha$$² = 0

$$\alpha$$² + $$\beta$$² = 1

$$\beta$$² = 1

$$\alpha$$⁴ = 0

$$\beta$$⁴ = 1

$$\alpha$$⁴ + $$\beta$$⁴ = 1