Dice $ T (x, y, z) = (xy, yz, xz) $, determine if $ T $ it is one on one and / or on.

So far, I have found a contradiction that proves $ T $ it is not one to one

$ T (-1, 1, -1) = (-1, -1, 1) $

Y, $ T (1, -1, 1) = (-1, -1, 1) $. However, I can not find out whether or not $ T $ is in … I think so, but I do not know why or how to prove it.

I can say:

Taking arbitrary elements a, b, c $ in mathbb R $, $ T (a, b, c) = (ab, bc, ac) $, and therefore any element $ x, y, z in mathbb R $ can be generated by $ x = ab $, $ y = bc $Y $ z = ac $?