Answer to Question #245714 in Electricity and Magnetism for hanata yuji

Electricity and Magnetism

Question #245714

show that [A,[B,C]]+[B,[C,A]]+[A,B]

Expert's answer

[A,[B,C]]+[B,[C,A]]+[A,B]

[A,(BC-CB)]+[B,(CA-AC)]+AB-BA

[A,BC]-[A,CB]+[B,CA]-[B,AC]+AB-BA

ABC-BCA -ACB+CBA +BCA-CAB -BAC-ACB +AB-BA

ABC -2ACB+CBA +-CAB -BAC +AB-BA

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