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
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
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.
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.
If you love our answers, you can simply join our community and also provide answers like this, fellow learners like you will appreciate it.
/ culled from 2021 JAMB-UTME MATHEMATICS question 34 /