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JAMB Mathematics 2021 Paper

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Question : 34

Total: 40

If the binary operation

*

is defined by m

*

n = mn + m + n for any real number m and n, find the identity of the elements under this operation

e = 1
e = -1
e = -2
e = 0

Solution:

Concept:

An identity element

e

satisfies

m * e = m

for every real number

m

.

Explanation:

Given

m * n = mn + m + n

, replace

n

with

e

.

So

m * e = me + m + e

.

Since

e

is the identity,

m * e = m

.

Therefore,

me + m + e = m

.

Subtract

m

from both sides:

me + e = 0

.

Factor:

e(m + 1) = 0

.

For this to hold for all real

m

, we must have

e = 0

.

Answer:

The identity element is

e = 0

, which is option D.

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