Group homomorphisms functions

Homomorphism
Problem 4:
Let G, G1, and G2 be groups. Let µ1 : G -> G1 and µ2 : G -> G2 be group homomorphisms. Prove that
µ : G -> G1 × G2 defined by :
µ (x) = (µ1 (x), µ2 (x)), for all x in G,
is a well-defined group homomorphism.

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...in G, we have
µ (a b) = ( µ1 (ab), µ2 (ab) ) = ( µ1 (a) µ1 (b), µ2 (a) ...