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

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

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

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

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

If \[A=\left[ \begin{matrix} a & b \\ b & a \\ \end{matrix} \right]\

1.	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.	\[\alpha =2ab,\beta ={{a}^{2}}+{{b}^{2}}\]
B.	\[\alpha ={{a}^{2}}+{{b}^{2}},\beta =ab\]
C.	\[\alpha ={{a}^{2}}+{{b}^{2}},\beta =2ab\]
D.	\[\alpha ={{a}^{2}}+{{b}^{2}},\beta ={{a}^{2}}-{{b}^{2}}\]
Answer» D. \[\alpha ={{a}^{2}}+{{b}^{2}},\beta ={{a}^{2}}-{{b}^{2}}\]

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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

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