Every nonzero element has a unique multiplicative inverse

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Prove that in any field F, every nonzero element has a unique multiplicative inverse. In other words, if a is any nonzero element of F and b and c are any elements of F such that ab = ac = 1, then b = c. This fact enables us to speak of "the multiplicative inverse" rather than "a multiplicative inverse" of a nonzero element in a field.

Reference no: EM131178632

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