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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 in` Z` with respect to * such that
`a ** e=a=e ** a, forall a in Z `
` a **e=a { and } e ** a=a, forall a in Z `
` a+e-5=a { and } e+a-5=a, forall a in Z `
` e=5, forall a in Z`
Thus, `5 `is the identity element in `Z `with respect to *.
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