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If the binary operation * on the set Z i...

If the binary operation * on the set Z is defined by a*b`=a+b-5,` then find the identity element with respect to *.

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Let `e` be the identity element.
Then according to the definition of the identity element we get, `a∗e=e∗a=a` for all `a in Z`.
Then we have, `a+e−5=a` or, `e=5`.
So the identity element is `5`.
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