Let G = (G, . , e), H = (H , * , E) be groups ... (e is the identity)

the direct product is defined by:

G x H = (GXH, o , (e,E)) where,

(g1,h1) o (g2,h2) = (g1 . g2, h1*h2)

Question: Show formally that G x H is a group.

when it says, "show formally that G x H is a group".. does it mean show that G x H satisfies the 4 conditions for being a group.. i.e.

associativity,

closure,

existance of identity element and

existance of inverse element?

any help is appreciated..