Let $$\alpha$$ and $$\beta$$ be real numbers. Consider a $$3 \times 3$$ matrix $$A$$ such that $$A^2 = 3A + \alpha I$$. If $$A^4 = 21A + \beta I$$, then

A

$$\alpha = 1$$

B

$$\alpha = 4$$

C

$$\beta = 8$$

D

$$\beta = -8$$