In the set of integers $(Z, *)$,if $a * b = a + b - n, \forall a, b \in Z$,where $n$ is a fixed integer,then the inverse of $(-n)$ is:

Consider the binary operation $\wedge$ on the set $\{1, 2, 3, 4, 5\}$ defined by $a \wedge b = \min\{a, b\}$. Write the operation table of the operation $\wedge$.

For each binary operation $^*$ defined below,determine whether $^*$ is commutative or associative. On $Z^+$,define $a ^* b = a^b$.

Consider a binary operation $*$ on the set $\{1,2,3,4,5\}$ given by the following multiplication table. Is $^*$ commutative?
(Hint: use the following table)

$^*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$2$	$2$	$2$
$3$	$1$	$2$	$3$	$3$	$3$
$4$	$1$	$2$	$3$	$4$	$4$
$5$	$1$	$2$	$3$	$4$	$5$

On the set of all natural numbers $N$,which one of the following $*$ is a binary operation?

Let $*$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a * b = (a - b)^{2}$ for all $a, b \in Q$ is commutative.