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# The Jacobi Identity

LINALG-JLL4YX

If $A$, $B$, and $C$ are square matrices of the same size, and if one defines:

$$[A,B]=AB-BA$$

...then:

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

...equals:

A

$I$, the identity matrix

B

$0$, the zero matrix

C

$ABC$

D

$A+B+C$