Question

31. The set of integers z with the binary
operation defined as a* b = a+b+c
for a, b e z is a group. The identity
element of this group is :
(A)
0
(B) 1
(C) -1
(D)
12​

Answer 1

Answer:

-1

Step-by-step explanation:

a∗b=a+b+1   (a,b,z is a group)

at a=−1⇒a∗b=−1+b+1=b

at b=−1⇒a∗b=a−1+1=a

⇒a∗0=a+0+1

⇒ identity element is −1.