Show that if K is a field and x,yEK satify x≠0 and y≠0, then xy≠0? Where do I start?
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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 $\displaystyle \,xy = 0$. Then $\displaystyle x^{-1}xy = x^{-1}\cdot0 \implies y=0$. Contradiction.
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