Let R be a ring.
(a) Show that a.0 = 0.a = 0 for all a belongs toR.
(b) Using (a), show that for any a, b in R, (-a)b = -(ab):
(c) Using (b), show that for any a, b in R, (-a)(-b) = ab:
(a) so far I have done part (a) and showed that a.0 = 0.a = 0
and the steps are as follows:
We have 0+0 = 0, since 0 is the zero element. Multiply both sides by a:
a0+a0 = a(0+0) = a0 = a0+0;
where the last equality uses the zero law again. Now from
a0+a0 = a0+0, we get a0 = 0 by the cancellation law. The other part 0a = 0 is proved similarly.
But I couldnt do part (b) and (c) help would be appreciated thank you..