on the set N of natural numbers there is Commutative binary operation that is marked as *. it is known that N is a group under *, 2 is a Identity element and that 3 is an inverse of 1 in the group. for N we define another binary operation called Δ which is defined for a,b∈N as aΔb=(a*1)*b. prove that N is a group under the operation Δ.
this is a question i have in homework, what should i do?. prove that N under Δ have Closure,Associativity,Identity element and Inverse element?. i think i found the identity element of Δ(3) but i don't sure about how to prove it, i need to write something like "3Δb=(3*1)* b=e*b=b and since N is associative under *, (a*1)* b=a*(1*b) so aΔ3=(a*1)* 3=a*(1*3)=a*e=a"?.