If A = begin{bmatrix} a & b b & a end{bmatri | vedclass

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(B) Given $A = \begin{bmatrix} a & b \ b & a \end{bmatrix}$.We need to find $A^2 = A 	imes A$.$A^2 = \begin{bmatrix} a & b \ b & a \end{bmatrix} \b

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$\alpha = a^2 + b^2, \beta = 2ab$

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(B) Given $A = \begin{bmatrix} a & b \ b & a \end{bmatrix}$.We need to find $A^2 = A 	imes A$.$A^2 = \begin{bmatrix} a & b \ b & a \end{bmatrix} \begin{bmatrix} a & b \ b & a \end{bmatrix} = \begin{bmatrix} a^2 + b^2 & ab + ba \ ba + ab & b^2 + a^2 \end{bmatrix}$.$A^2 = \begin{bmatrix} a^2 + b^2 & 2ab \ 2ab & a^2 + b^2 \end{bmatrix}$.Comparing this with $A^2 = \begin{bmatrix} \alpha & \beta \ \beta & \alpha \end{bmatrix}$,we get $\alpha = a^2 + b^2$ and $\beta = 2ab$.

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

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