Good morning. Please i need a help to solve the following exercises:

1. Let f: Q --> Q be an homomorfism. Prove that, or f(x)=0 for all x in Q or then f(x) =x for all x in Q

2. Let A, B be sets of positive reals numbers. Letīs define A.B={x.y; x belong to A and y belong to B}. Prove that if A and B are limited, then A.B is limited, where supreme (A.B)=suprmeA.supremeB and inf(A.B)=infA.infB