My submission for the most outlandish/outrageous solution:

   minors=: 1&(|:\.)"2^:2
   det=: -/ .*
   (<0 1) |: det minors (* =@/:) 3 1 4 1 5 9
180 540 135 540 108 60

As usual, when referring to minors, the obligatory Green Mug link:
http://www.jsoftware.com/jwiki/DavidMitchell
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