question_answer

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

A)  \[\alpha ={{a}^{2}}+{{b}^{2}},\]\[\beta =ab\]

B)  \[\alpha =2ab,\]\[\beta ={{a}^{2}}+{{b}^{2}}\]

C)  \[\alpha ={{a}^{2}}+{{b}^{2}},\]\[\beta ={{a}^{2}}-{{b}^{2}}\]

D)  \[\alpha ={{a}^{2}}+{{b}^{2}},\]\[\beta =2ab\]

E)  None of these