Question

Find which of the operations given above has identity.

Answer 1

The given operations are,

(i) a∗b=a−b

(ii) a∗b= a 2 + b 2

(iii) a∗b=a+ab

(iv) a∗b= ( a−b ) 2

(v) a∗b= ab 4

(vi) a∗b=a b 2

An element e∈Q is said to be an identity element of the operation if the following condition is satisfied,

a∗e=a e∗a=a

In part (v), consider b=e,

ae 4 =a e=4

And,

ea 4 =a e=4

There is an element e=4∈Q that exists with respect to the given operation which satisfies the condition of an identity element.

Thus, the operation a∗b= ab 4 has identity.