Re: proof of (-1).a= -a

Noh wrote:

0.a = 0.a + 0
  = 0.a + 0.-a
  = 0.(a+ -a)
  = 0.0
  = 0


Therefore, when proving that one always has 0.a = 0, you've used the
fact that 0.(-a) = 0. Don't you see a problem here?

I would do as follows:

0.a = (0 + 0).a = 0.a + 0.a.

Now, adding -(0.a) to both sides you get that 0 = 0.a.

Best regards,

Jose Carlos Santos
.