Question

Let ∗ be a binary operation on the set Q of rational numbers as follows:

(i) a ∗ b = a – b
(ii) a ∗ b = a²+ b²

(iii) a ∗ b = a + ab
(iv) a ∗ b = (a – b)
²

(v) a ∗ b = 4
ab

(vi) a ∗ b = ab²
Find which of the operations given above has identity.
PLEASE ANSWER THIS QUESTION WITH EXPLANATION​

Answer 1

Answer:

Step-by-step explanation:

given * be the binary operation on Q

let a=1/2

b=3/4

now

i) a*b=a-b=1/2-3/4=-1/4

ii) a*b=a^2+b^2=(1/2)+(9/16)=8+9/16=17/16

iii) a*b=a+ab=(1/2)+(1/2)*(3/4)=(1/2)+(3/8)=7/8

iv) a*b=a-b)^2=(-1/4)^2=1/16

v) a*b=4*(1/2)*(3/4)=3/2

vi) a*b=ab^2=(1/2)(9/16)=9/32

the additive identity is zero for rational numbers