If we denote the identity by e, then for any a in Q:
we have a*e=a+e+3ae=a
thus e=0.
gives the formula of the inverse of a.
a has no inverse iff 1+3a=0.
Show that *,defined on Q (where Q is a set of rational numbers) by
a * b = a + b + 3ab
is a commutative binary operation.Is is associative?
Ive answered this part but i dont know how to answer part b
Determine the identity element admitted by * and show that it is unique.Show that with respect to this identity the inverse a(^ -1) of a is given by
a(^ -1) = ((-a)/(1+3a))
Give an element a C Q which has no inverse with respect to *.
(where C means contained, Q is a set of rational numbers)