\[\](1)An element of a group can have more then one inverse.\[\](2)If every element of a group is its own inverse , then the group is abelian.\[\](3)The set of all $2\times 2$ real matrices forms a group under matrix multiplication.\[\](4)$(a^{\ast} b)^{-1}=a^{-1} \ast b^{-1}$ for all $a,b\in G$