An operation * is defined on the set of real numbers by a * b = ab + 2(a + b + 1). find the identity element
A
2
B
1
C
-1
D
-2
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
a * b = ab + 2(a + b + 1)
let e be the identity element
∴ a * e = e * a = a
∴ a * e = a
ae + 2(a + e + 1) = a
ae + 2a + 2e + 2 = a
ae + 2e = a - 2a = 2
(a + 2)e = -a - 2
e = -a-2 / (a+2)
e = -(a+2) / (a+2)
e = -1
Source: Myschool Past Questions Archive (Record #8324)