Consider the group G={x∈R such thatx≠0} under the binary operation *: The identify element of G is e=−12. The order of the element +2 is: a) 3 b) ∞ c) 2 d) 1

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Consider the group G={x∈R such thatx≠0} under the binary operation *: The identify element of G is e=−12. The order of the element +2 is: a) 3 b) ∞ c) 2 d) 1

Glenn Cooper · Accepted Answer

Problem overview and setting mathematical relationship We know that, Every element of G must satisfy the basic condition that it should be equal to en where n is some integer which is referred here as order and e is the identity element of G (here e=−12) So, now, we have to find order, we just equate en with +2 and solve to find n and that&#039;s all. Mathematical equation So, writing the mathematical form of above discussion, en=+2 (−12)n=2 Taking logarithm of both sides nlog⁡(−12)=log⁡(2) n=log⁡(2)÷log⁡(−12) n= undefined ( because logarithm of negative fractions are not part of R ) Hence, order should tend to exist at infinity. So, answer is (option 2) ∞

Consider the group G=\{x \in R \text{such that} x \ne 0\} under

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