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Question
The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is ______.
Options
1
0
2
none of these
Solution
The identity element for the binary operation * defined on Q ~ {0} as a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0} is 2.
Explanation:
Given that, a * b = `"ab"/2` ∀ a, b ∈ Q ~ {0}
Let e be the identify element for *
∴ a * e = `"ae"/2`
⇒ a = `"ae"/2`
⇒ e = 2
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