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Earlier discussion
3 older comments kept for context.
Oluwaseun Adeyemi
m \(\ast\) n = mn + m + n
m \(\ast\) e = me + m + e, e \(\ast\) m = e
∴ me + m + e, m(e + 1)e - e = 0
e + 1 = 0
∴ e = -1
Sani Abdulkadir
No, this is wrong!
If mn=mn+m+n
let e be the identity, so
me=m because multiplicative identity is 1, and any number multiply by 1 is the same number.
So, if m*e=m, then we will have
m=me + m + e
>>> m-m= me+e
>>> 0=e(m+1)
e= 0/(m+1)
e=0.
Lawrence
Yh it is wrong