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Find identity element
Given:
\( a * b = a + b – 5, \quad a,b \in \mathbb{Z} \)
Identity Definition:
\( a * e = a = e * a \)
Find \( e \):
\( a * e = a + e – 5 = a \)
Simplify:
\( a + e – 5 = a \Rightarrow e = 5 \)
Verification:
\( a * 5 = a + 5 – 5 = a \)
\( 5 * a = 5 + a – 5 = a \)
Conclusion:
✔ Identity element = 5