Checking associativity prop. of Group, in which order

Question

It is given here that depending on situation, need to check the property of associativity before or after that of checking that of identity and inverse (effectively, identity, as the page further says that identity need be found before inverse). I have new clue to know further there. Also, submitting an image of the same page:

Answer 1

If you're asking how to check the associativity of these, it's pretty simple.

$(x*y)*z = (x+y+46)*z = (x+y+46)+z+46 = x+y+z+92$

$x*(y*z)$ can be easily computed using the same logic.