Matrices and Determinants: JEE Main 2021 Mathematics question

Let P = $\left[ {\matrix{ 3 & { - 1} & { - 2} \cr 2 & 0 & \alpha \cr 3 & { - 5} & 0 \cr } } \right]$, where $\alpha$ $\in$ R. Suppose Q = [ q_ij] is a matrix satisfying PQ = kl₃ for some non-zero k $\in$ R. If q₂₃ = $- {k \over 8}$ and |Q| = ${{{k^2}} \over 2}$, then a² + k² is equal to ______.