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Let * be a binary operation on Z defined by a * b = a + b – 15 for a, b ∈ Z. The inverse of element 21 in (Z, *) is

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Let a ∈ Z and b be its inverse 

∴ a * b = e = b * a 

⇒ a + b – 15 = 15 = b + a – 15 

⇒ b = 30 – a ∈ Z 

∴ The inverse of a ∈ Z is 30 – a 

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