Let $P=\left[\begin{array}{ccc}3& -1& -2\\ 2& 0& \alpha \\ 3& -5& 0\end{array}\right]$ , where $\alpha \in R,$ Suppose $Q=\left[q_{ij}\right]$ is a matrix such that $PQ=kI$, where $k\in R, k\ne 0$ and $I$ is the identity matrix of order $3$. If $q_{23}=-\frac{k}{8}$ and $\det \left(Q\right)=\frac{k^2}{2}$ then