Does AB=0 necessarily mean BA=0?

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Homework Statement


If two operators have no inverse operators, but satisfy:
[tex]AB=0[/tex]
is it true that [tex]BA=0[/tex]? And how would we go to prove this?
 

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No, it's not true. Fiddle around with 2x2 matrices and try to discover a counterexample.
 

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