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Q)

Which of the following is correct?

(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 $a,b\in G$

The matrix $\begin {bmatrix} a & a \\a & a \end{bmatrix}$ is a $2 \times 2$ matrix
$(a^{\ast} b)^{-1}=b^{-1} \ast a^{-1}$ for all $a,b\in G$