JEE Math Practice Question

If $$A = \left[ {\begin{matrix} a & b \\ b & a \\ \end{matrix} } \right]$$ and $${A^2} = \left[ {\begin{matrix} \alpha & \beta \\ \beta & \alpha \\ \end{matrix} } \right]$$, then

1. A.$$\alpha = 2ab,\,\beta = {a^2} + {b^2}$$
2. B.$$\alpha = {a^2} + {b^2},\,\beta = ab$$
3. C.$$\alpha = {a^2} + {b^2},\,\beta = 2ab$$
4. D.$$\alpha = {a^2} + {b^2},\,\beta = {a^2} - {b^2}$$