_Is it an isomorphism?_

Suppose that someone tells you that their category \$$C \$$ has two objects \$$c,d \$$ and two non-identity morphisms, \$$f : c \to d \$$ and \$$g : d \to c \$$, but no other morphisms. Does \$$f \$$ have to be the inverse of \$$g \$$, i.e. is it forced by the category axioms that \$$g◦f = id_c \$$ and \$$f◦g= id_d \$$?