Let $*$ denote an operation, assigning a real number $a * b$ to each pair of real numbers ( $a, b)$ (e.g., $a * b=$ $a+b^{2}-17$ ). Devise an equation which is true (for all possible values of variables) provided the operation $*$ is commutative or associative and which can be false otherwise.
A suitable equation is $x *(x * x)=(x * x) * x$ which is obviously true if $*$ is any commutative or associative operation but does not hold in general, e.g., $1-(1-1) \neq(1-1)-1$.