If \( \alpha, \beta, \gamma \) are three real numbers and \( A=\lef...

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If \( \alpha, \beta, \gamma \) are three real numbers and \( A=\left[\begin{array}{ccc}1 & \cos (\alpha-\beta) & \cos (\alpha-\gamma) \\ \cos (\beta-\alpha) & 1 & \cos (\beta-\gamma) \\ \cos (\gamma-\alpha) & \cos (\gamma-\beta) & 1\end{array}\right] \), then:
 
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