Need help proving a couple theorems

Prove the following theorems.

1) If *x *is any number, then 0**x* = 0.

2) If *x *is any number, there do not exist two numbers *y* and *y'* such that *x***y* = 1 and *x***y'* = 1.

Use any of the following axioms to help prove the above theorems:

1) If each of *x* and *y* is a number, then *x*y* is a number.

2) If each of *x *and *y* is a number, then *x*y = y*x.*

3) If each of *x*, *y*, and *z* is a number, then (*x*y*)**z* = *x**(*y*z*).

4) There is a number *U* such that if *x *is any number, then *U*x = x.*