Invertible Element Binary Operation
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Q.
If a ∗ b = a = b ∗ a, then b is called the inverse of a under the operation ∗
True
False
Q. Let * be a binary operation on set Q − {1} defined bya * b = a + b − ab for all a, b ∈ Q − {1}.
Then, which of the following statement(s) is/are true?
Then, which of the following statement(s) is/are true?
- 0 is the identity element with respect to * on Q−{1}.
- Every element of Q− {1} is invertible.
- For any element a∈Q−{1}, inverse of a is aa−1
- * is associative on Q− {1}