Question

Define \( \oplus \text{ on } \mathbb{R} X \mathbb{R} \) by setting \( (a,b) \oplus (c,d)=(ac-bd, ad+bc) \)
Show that \( ( \mathbb{R} X \mathbb{R} , \oplus ) \) is an algebraic system

Answer 1

@eliassaab I have not touched rings or fields yet how wld i show that it is an algebraic system

Answer 2

This cant be a group since (0,0) doesnt have a unique inverse