I am working on this problem in which I have a theory T based on L language and the only information we have is that **T is consistent** and * |- not(A -> A)*. Given this information, how can I know if this theory is sound, complete and/or decidable?

My only guess is that I can say that T is sound because since T is consistent and we can derive * not(A->A)* from axioms and inference rules,

*is a theorem and because of that we can assume that T is sound (because the premises and conclusions are true).*

**not(A->A)**Am I correct? What else can I tell about this theory?

Thank you!