Check the commutativity and associativity of * on `N` defined by `a*b=gcd(a ,\ b)` for all `a ,\ b in N` .

Explanation

* on `N`
defined by `a`*`b=gcd(a ,\ b)`
for all `a ,\ b in N`

Then we have check the commutativity and associativity of *

`a`*`b=gcd(a,b)`

`b`*`a=gcd(b,a)`

`a`*`b=b`*`a`

Now let `a,b,c in N`

...