Question

If a binary operation * on the set Z of integers is defined by a*b = a+b-5, then find the identity element for the
operation
​

Answer 1

Answer:

            5

Step-by-step explanation:

The identity element is the element e such that a*e = a and e*b = b.

Now...

a*e = a   ⇒   a+e-5 = a   ⇒   e-5 = 0   ⇒   e = 5

Checking that the other property is also satisfied by this:

e*b = 5*b = 5+b-5 = b   ✓

So the identity element is 5.