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.
Last updated at Oct. 1, 2019 by Teachoo
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.
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
CBSE Class 12 Sample Paper for 2019 Boards
Question 1
Question 2
Question 3
Question 4 (Or 1st)
Question 4 (Or 2nd)
Question 5 You are here
Question 6
Question 7
Question 8 (Or 1st)
Question 8 (Or 2nd)
Question 9
Question 10 (Or 1st)
Question 10 (Or 2nd)
Question 11
Question 12 (Or 1st)
Question 12 (Or 2nd)
Question 13 (Or 1st)
Question 13 (Or 2nd)
Question 14
Question 15
Question 16 (Or 1st)
Question 16 (Or 2nd)
Question 17
Question 18
Question 19
Question 20
Question 21 (Or 1st)
Question 21 (Or 2nd)
Question 22
Question 23
Question 24 (Or 1st)
Question 24 (Or 2nd)
Question 25
Question 26 (Or 1st)
Question 26 (Or 2nd)
Question 27 (Or 1st)
Question 27 (Or 2nd)
Question 28
Question 29
CBSE Class 12 Sample Paper for 2019 Boards
About the Author