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

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 ______.

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