Originally Posted by
meggnog Prove that in any ring R, 0 x a = 0 for all real numbers a.
"For all REAL numbers..."?? What have real numbers to do here if R is a general ring? Read again CAREFULLY the axioms of ring theory and then use here that $\displaystyle a\cdot 0 = a(0+0)=$ ...
Also prove that in any ring R,
(-1)a = -a for all real numbers a.