I know sup(AB) = sup(A)sup(B) if A and B are nonnegative, but what if the assumption is dropped that A and B are nonnegative. Does this change the answer?

I know sup(AB) = sup(A)sup(B) if A and B are nonnegative, but what if the assumption is dropped that A and B are nonnegative. Does this change the answer?

Please tell us what are A & B? In what sense are they nonnegative?
Just define your terms.