The set $\{-1, 0, 1\}$ is not a multiplicative group because of the failure of

If $A = \{a, b, c\}$,then the number of binary operations on $A$ is

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a * b = a + ab$. Is the operation $^*$ commutative and associative?

For each binary operation $^*$ defined below,determine whether $^*$ is commutative or associative. On $Q$,define $a ^* b = ab + 1$.

On the set of positive rationals,a binary operation $*$ is defined by $a * b = \frac{2ab}{5}$. If $2 * x = 3^{-1}$,then $x = $

Show that $*: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$ defined by $a * b = a + 2b$ is not commutative.