# Ex 1.4, 11

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 1.4, 11 Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Show that * is commutative and associative. Find the identity element for * on A, if any. Check commutative * is commutative if (a, b) * (c, d) = (c, d) * (a, b) ∀ a, b, c, d ∈ R Since (a, b) * (c, d) = (c, d) * (a, b) ∀ a, b, c, d ∈ R * is commutative (a, b) * (c, d) = (a + c, b + d) Check associative * is associative if (a, b) * ( (c, d) * (x, y) ) = ((a, b) * (c, d)) * (x, y) ∀ a, b, c, d, x, y ∈ R Since (a, b) * ( (c, d) * (x, y) ) = ((a, b) * (c, d)) * (x, y) ∀ a, b, c, d, x, y ∈ R * is associative (a, b) * (c, d) = (a + c, b + d) Identity element e is identity of * if (a, b) * e = e * (a, b) = (a, b) where e = (x, y) So, (a, b) * (x, y) = (x, y) * (a, b) = (a, b) (a + x, b + y) = (x + a , b + y) = (a, b) Now, (a + x, b + y) = (a, b) Comparing Therefore, the operation * does not have any identity element.

Ex 1.2, 5
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Example 23 Important

Example 25 Important

Ex 1.3, 3 Important

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Ex 1.4, 11 Important You are here

Misc 3 Important

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Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

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.