Data Sufficiency

If x is not equal to zero, is |x|<1? $$(1)\ \ \ \ x^2<1\ $$ $$(2)\ \ \ |x|<\frac{1}{x}$$ The OA is the option D.

I know how to prove that statement (1) is sufficient but, how can I prove that the second statement is sufficient?

Experts, I ask for your help.

Thanks in advanced.