Try This: Which of the following binary operations satisfy commutativity? Associativity? Existence of Identity?

$a**b=|a-b|$ on $Z_{?}0$

$a**b=a$ on $R$

$o+$ on $Z_8$

$ox$ on $Z_7-\{0\}$

$a**b=2(a+b)$ on $Z$