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I came across the following statement:

If $A$ and $B$ commute and $B$ and $C$ commute, do $A$ and $C$ necessarily commute? Prove or disprove.

Help.

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  • $\begingroup$ "an operator identity" is a pointless title. please give your questions informative titles. $\endgroup$ Sep 24, 2016 at 18:29

1 Answer 1

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Choose $B$ as the identity operator and $A$ and $C$ any operators that don't commute.

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    $\begingroup$ Alternatively, take $B=0$. $\endgroup$
    – Arnaud D.
    Sep 24, 2016 at 20:23
  • $\begingroup$ Good idea. I didn't think of that. $\endgroup$
    – Kaligule
    Sep 24, 2016 at 20:35

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