# Question: let be a binary operation on a set s...

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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 inverse and a right inverse under * then left inverse and right inverse are equal.