If the binary operation * on the set Z of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.
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If the binary operation * on the set Z of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.

If the binary operation * on the set Z of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.
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If the binary operation $*$ on the set $Z$ of integers is defined by $a * b=a+b-5$, then write the identity element for the operation * in Z.
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SOLUTION : Let $\mathrm{e}$ be identity element, then $\mathrm{a} \cdot \mathrm{e}=\mathrm{e} * \mathrm{a}=\mathrm{a}$

$\Rightarrow \quad \mathrm{a}+\mathrm{e}-5=\mathrm{e}+\mathrm{a}-5=\mathrm{a} \quad \Rightarrow \quad \mathrm{e}=5$

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