If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$, then :

Question

( A ) $\alpha = a^2 + b^2, \; \beta = a^2-b^2$
( B ) $\alpha = 2ab, \; \beta = a^2+b^2$
( C ) $\alpha = a^2 +b^2, \; \beta = ab$
( D ) $\alpha = a^2 + b^2, \; \beta = 2ab$