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Example 39 - Chapter 1 Class 12 Relation and Functions - Part 2

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Example 39 Show that – a is the inverse of a for the addition operation ‘+’ on R and 1﷮a﷯ is the inverse of a ≠ 0 for the multiplication operation ‘×’ on R. Addition An element a in R is invertible if, there is an element b in R such that , a * b = e = b * a Here, b is the inverse of a Here, e = 0 for addition So, a * b = e = b * a a + b = 0 = b + a ⇒ b = –a Since a + (– a) = 0 = (– a) + a = 0, So, –a is the inverse of a for addition. Multiplication An element a in R is invertible if, there is an element b in R such that , a * b = e = b * a Here, b is the inverse of a Here, e = 1 for multiplication So, a * b = e = b * a a × b = 1 = b × a ⇒ b = 1﷮𝑎﷯ Since a × 1﷮𝑎﷯ = 1 = 1﷮𝑎﷯ × a So, 𝟏﷮𝒂﷯ is the inverse of a for addition.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.