## JEE Advanced 2016 Paper 1 Mathematics Question 44

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

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