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**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**

**A.**** e = 1**

**B.**** e = -1**

**C.**** e = -2**

**D.**** e = 0**

**QUICK ANSWER…**

**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**

**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:**

**Option A is incorrect.****Option B is not correct.****C is incorrect.****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 20****21**** JAMB-UTME**** MATHEMATICS**** question**** 34 ****/**