If the binary operation \(\ast\) is defined by m \(\ast\) 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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Identity(e) : a \(\ast\) e = a
m \(\ast\) e = m...(i)
m \(\ast\) e = me + m + e
Because m \(\ast\) e = m
: m = me + m + e
m - m = e(m + 1)
e = \(\frac{0}{m + 1}\)
e = 0
Source: WAEC / JAMB / NECO Classroom Archive (Record #60728)