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Let \( P=\left[\begin{array}{rrr}3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0\end{array}\right] \), where \( \alpha \in R \). Suppose \( Q=\left[q_{i j}\right] \) is a matrix satisfying \( P Q=k I_{3} \) for some non-zero \( k \in R \). If \( q_{23}=-\frac{k}{8} \) and \( |Q|=\frac{k^{2}}{2} \), then \( \alpha^{2}+k^{2} \) is equal to
\( \mathrm{P} \)
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