Let `**` be binary operation on N defined by `a ** b` = L.C.M. of a and b. Find
(i) Identify element of `**` in N
(ii) Elements of N which are invertible to the operation *

Explanation

(i) For identity element 'e'
`a** e = e ** a = a`
`rArr` L.C.M. of a and e= a
i.e., e = 1
Therefore identity element on N is 1.
(ii) Now as identity element exists so we can find invertibility
Now, element a is said to be invertible if there exist element c on N such that `a ** c = c ** a = e = 1`
i.e., L.C.M. of 'a' and 'c' is 1
`rArr` a has to be 1 and c has to be 1
So, a = 1 is only element on N which is invertible for operation *