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Carlo Beenakker
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Does this one-line proof qualify?

$$1={\rm Pf}\,\Omega={\rm Pf}\, (M^T \Omega M) = ({\rm Det}\,M)\,({\rm Pf}\,\Omega)={\rm Det}\,M,$$ where I have used the defining property $M^T \Omega M=\Omega$ with $\Omega={{0\;\;I}\choose{-I\;0}}$.

Carlo Beenakker
  • 188.1k
  • 18
  • 448
  • 651