# If the binary operation ∗ is defined by m ∗ n =…

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A. e = 1

B. e = -1

C. e = -2

D. e = 0

D

## DETAILS…

If the binary operation  is defined by m  n = mn + m + n for any real number m and n, the identity of the elements under this operation will be = zero, let’s get the details below.

Please before we proceed, note that for all binary operations like * or ꚛ, e is the identity element if and only is one condition is met, that condition is:

• a * e = a
RELATED!  A binary operation Ꚛ is defined by m Ꚛ n = mn + m – n

so, performing m * e = m, or n * e = n, we should be able to derive e.

so, by the operation featured in this question, m * e = me + m + e,

but according to our condition, m * e = m

thus,

me + m + e = m

me + e = m – m

me + e = 0

e(m + 1) = 0

e = 0/(m + 1)

e = 0

please note that solving with n will give the same thing as in:

n * e = ne + n + e = n

e = 0/(n + 1)

e = 0

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is not correct.
3. C is incorrect.
4. D is the correct answer.

## KEY-POINTS…

You may please note these/this:

• In binary operations, the identity element can be derived by following one condition.
• This condition is a * e = a.
• Where a = one of the main elements, and e = the identity element.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 34 /

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