If operators $A$ and $B$ commute and $B$ and $C$ commute, do $A$ and $C$ necessarily commute? 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.

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