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Binary operations: Inverse
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Binary operations: Inverse
Last updated at May 29, 2023 by Teachoo
Question 25 Show that the number of binary operations on {1, 2} having 1 as identity and having 2 as the inverse of 2 is exactly one. Given that 1 is identity e is the identity of * if a * e = e * a = a So, a * 1 = 1 * a = a Put a = 1 1 * 1 = 1 Put a = 2 1 * 2 = 2 * 1 = 1 Also, Given that 2 is inverse of 2 b is the inverse of a if a * b = b * a = e Here, e = 1 & a = 2, b = 2 So, 2 * 2 = 2 * 2 = 1 Hence, there is only 1 binary operation which satisfies the given conditions