Let * be a binary operation on a set S. Assume the domain of definition of * is S^2, assume * is associative and n is the neutral element for *. Now, let s and t be two elements of S. We say that t is a left inverse of s under * iff t*s=n. We say that t is a right inverse of s iff s*t=n. Show that if an element of S has both a left and right inverse under * then the left inverse and the right inverse are equal.
closed as off-topic by This is much healthier., Jyrki Lahtonen, RecklessReckoner, Claude Leibovici, glace Jul 14 at 7:56
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