CBSE Class 12 Sample Paper for 2019 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 5 - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

Question 5

Let A = Z × Z and * be a binary operation on A defined by

  (a, b)*(c, d) = (ad + bc, bd).

Find the identity element for * in the set A.

Let A = Z x Z and * be a binary operation on A defined by (a, b)*(c,d)

Question 5 - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 5 - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

Transcript

Question 5 Let A = Z × Z and * be a binary operation on A defined by (a, b)*(c, d) = (ad + bc, bd). Find the identity element for * in the set A. Let e be the identity element for * in set A e is the identity of A if (a, b) * e = e * (a, b) = (a, b) Here, e = (x, y) Now, (a, b) * (x, y) = (x, y) * (a, b) = (a, b) (ay + bx, by) = (xb + ya, yb) = (a, b) Comparing ay + bx = a by = b y = 𝑏/𝑏 y = 1 Comparing Putting y = 1 in (1) ay + bx = a a × 1 + bx = a a + bx = a bx = a – a bx = 0 x = 0 So, x = 0, y = 1 ∴ e = (x, y) = (0, 1) is the identity element

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.