Let *, be a binary operation on N, the set of natural numbers defined by `a*b = a^b`, for all `a,b in N`. is * associative or commutative on N?

Explanation

Here, `a times b=a b`

for all `a, b in {N}.`

Now,` a times b=a b and b times a=b a.`

therefore `a * b equiv b * a.`

So, given operation is not associative.