Question 1 of 11 Consider the following groups (1) Let G₁-R-{-1}. Define a binary operation on G₁ as follows: For any a, b G we have that a b-a+b+ab. (2) Let G₂= ={( }). a, beR.Define a binary operation on G₂ as follows: For any matrices ( ) and ( }) (i) in G₂ we have that (1 1) (1 1)-(+° b+a). a+c 1 B (3) Let G3 - {(1,2),z=R}. Define a binary operation on G₁ by (1,z) • (1, y) − (1, x + y). Which of the following statements is/are true? ㅁㅁㅁ A. The inverse of 1 in G₁ under is given by The identity element of Gs under is given by (1, 1) C. The inverse of 1 in G, under is given by 1 D. The identity element of G₂ under is given by The inverse of the matrix *(})" in G₂ under given by The identity element of Gs under is given by (1,0) a. The identity element of Ga under @ is given by (2)- ☐ A Question 711 Latga 234567891011 12 7 32 10 11 46 aj Wree in cycle notation and then complete the following K2 X1 X2 10 bi Write as a product of transpositions and then complete the following X3 Which elementified by d) is even or odd? Question 2 of 11 == GL(2, R). G is a group under multiplication of matrices. Consider the following subsets of G : 1 H = {(69). (69)} -1 0 and K = 0 -1 1 n {(b): nez}. Which one of the following statements is true? A. K is a subgroup of H. B. K is a subgroup of G and for any A = (67) C. H is a subgroup of G. Reset Selection ЄK we have that A1 = (249).