1.

Let a* b =1cm (a,b) for all values of a,b in N (i) Find (12*16) (ii) Show that* is commutative on N (iii) Find the identity element in N (iv) Find all invertible elements in N

Answer»


Solution :(i) `12*16 =1CM (12,16)=(4xx3xx4)=48`
(ii)a*B=1cm (a,b) =1cm (b,a)=b*a
(iii) let e be the identity element in N
(iv) Let a in N be an ARBITRARY element
Then `a*b=1 rarr 1cm (a,b)=1 rarr a=b=1`
`therefore` 1 is the only element in N which is ivertible


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