Question

determine whether the binary operation *on the set N of natural number defined by a*b=2ab is associative or not.

Answer 1

let G be a non empty set and * be an operation defined on G then it will follow associative property i.e.
(a*b)*c = a*(b*c)
using given operation
(2ab)*c=a*(2bc)
2[2abc] =2[2abc]
4abc= 4abc
therefore it will follow associative property