# Simple Field Question.

• September 13th 2010, 07:22 AM
calculuskid1
Simple Field Question.
Show that if K is a field and x,yEK satify x≠0 and y≠0, then xy≠0? Where do I start?
• September 13th 2010, 07:29 AM
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Quote:

Originally Posted by calculuskid1
Show that if K is a field and x,yEK satify x≠0 and y≠0, then xy≠0? Where do I start?

Suppose $\,xy = 0$. Then $x^{-1}xy = x^{-1}\cdot0 \implies y=0$. Contradiction.