# How to recognize a Complete Set of Commuting Operators (CSCO)

A question about 'completeness'. These two operators are commuting, but I want to know more about their completeness.

How do you know if {H}, {B}, {H,B} and/or {$H^2$,B} are forming (a) Complete Set(s) of Commuting Operators?

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So the set {H,B} is a CSCO, but no other set is. Note that since $H^2=I$, the fourth set is identical to the second. Of the four sets only the 3rd one is CSCO.