If \(A=\left[\begin{array}{ll}a & b\\ b& a\end{array}\right]\) and \(A^2=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]\) then
Answer & explanation
Correct answer: option 2
\(A^2=\left[\begin{array}{ll}a & b\\ b& a\end{array}\right]\left[\begin{array}{ll}a & b\\ b& a\end{array}\right]=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]\)
$⇒\begin{bmatrix}a^2+b^2&2ab\\2ab&a^2+b^2\end{bmatrix}=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$
$\alpha=a^2+b^2$
$\beta=2ab$