$A$ group $(G, *)$ has $10$ elements. The minimum number of elements of $G$,which are their own inverses is

Which of the following is false?

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

In a group $(G, *)$,for some element $a$ of $G$,if $a^{2}=e$,where $e$ is the identity element,then

For the binary operation $^*$ defined on the set $R - \{-1\}$ by $a ^* b = \frac{a}{b+1}$,determine whether $^*$ is commutative or associative.

Show that $*: R \times R \rightarrow R$ given by $(a, b) \rightarrow a+4 b^{2}$ is a binary operation.