Misc 14 - Let a * b = { a + b, a + b - 6. Show 0 is identity - Binary operations: Inverse

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  1. Chapter 1 Class 12 Relation and Functions
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Misc 14 Define a binary operation *on the set {0, 1, 2, 3, 4, 5} as a * b = + , + <6 & + 6, + 6 Show that zero is the identity for this operation and each element a 0 of the set is invertible with 6 a being the inverse of a. e is the identity of * if a * e = e * a = a Now, we need to show that each element a 0 of the set is invertible with 6 a being the inverse of a. a * b = + , + <6 & + 6, + 6 An element a in set is invertible if, there is an element in set such that , a * b = e = b * a Putting b = 6 a So, a + b = a + (6 a) = 6 Since a + b 6 a * b = a + b 6 a * b = a * (6 a) = a + (6 a) 6 = 0 b * a = (6 a) * a = (6 a) + a 6 = 0 Since a * (6 a) = (6 a) * a = 0 Hence, each element a of the set is invertible with 6 a being the inverse of a.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.