If \( \mathrm{A} \) and \( \mathrm{B} \) are non-singular matrices ...
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If \( \mathrm{A} \) and \( \mathrm{B} \) are non-singular matrices of order three such that \( \operatorname{adj}(\mathrm{AB})=\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & \alpha & 1 \\ 1 & 1 & \alpha\end{array}\right] \) and \( \left|\mathrm{B}^{2} \mathrm{adj} \mathrm{A}\right|=\alpha^{2} \) \( +3 \alpha-8 \), then the value of \( \alpha \) is equal to
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