Use use the left-right distributive laws:
We know that (xy)+(-xy)=0 by definition.
That is -(xy) is an additive inverse.
We need to show that
And hence an additive inverse of xy.
By uniqueness we conclude that -(xy)=(-x)y.
In order to show that, meaning,
We use distrivutive laws,
(The other proofs are anagolus).
Let us argue by contradiction.c) if x is not equal to 0, then (1/x) is not equal to zero and 1/(1/x) = x
Which is false/