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

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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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.