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[1,aa^(2)-bc],[1,b^(2)-ca=],[1,cc^(2)-ab...

[1,aa^(2)-bc],[1,b^(2)-ca=],[1,cc^(2)-ab]

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Without expanding prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

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