LetA=⎝⎛a1a4a7a2a5a8a3a6a9⎠⎞detA=a1(a5(a9)−a6(a8))−a2(a4(a9)−a6(a7))+a3(a4(a8)−a5(a7))B=⎝⎛a1a4a7+2a1a2a5a8+2a2a3a6a9+2a3⎠⎞detB=a1(a5(a9+2a3)−a6(a8+2a2))−a2(a4(a9+2a3)−a6(a7+2a1))+a3(a4(a8+2a2)−a5(a7+2a1))=a1(a5(a9)−a6(a8))−a2(a4(a9)−a6(a7))+a3(a4(a8)−a5(a7))+2(a1a3a5−a1a2a6−a2a3a4+a1a2a6+a2a3a4−a1a3a5)=a1(a5(a9)−a6(a8))−a2(a4(a9)−a6(a7))+a3(a4(a8)−a5(a7))+2(0)=a1(a5(a9)−a6(a8))−a2(a4(a9)−a6(a7))+a3(a4(a8)−a5(a7))=detA∴detB=detA
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