A binary operation \ast on the set of real numbers is defined by a \ast b = a + b + 5. Wha… — JAMB UTME

A binary operation $\ast$ on the set of real numbers is defined by $a \ast b = a + b + 5$ . What is the identity element of this operation?

Answer: -5

The identity element of the binary operation is

-5

By the definition of an identity element

e

, the relation

a \ast e = a

must hold for all real numbers

a

. Applying the rule

a \ast b = a + b + 5

gives

a + e + 5 = a

. Subtracting

a

from both sides leads to

e + 5 = 0

, which gives

e = -5

Set up the identity element equation

a \ast e = a \implies a + e + 5 = a

By definition of an identity element, operating any element

a

with

e

yields

a

Solve the equation for

e

e = -5

Subtracting

a

from both sides gives

e + 5 = 0

, which yields

e = -5

Identity Element of a Binary Operation

Question