If A is a non singular square matrix, then the false statement among the following is

(1)   $\mathrm{AdjA}=\left|\mathrm{A}\right| {\mathrm{A}}^{-1}$

        ${\mathrm{A}}^{-1}=\frac{\mathrm{adjA}}{\left|\mathrm{A}\right|}$

        (1) is correct

(2)   ${\left(\mathrm{AdjA}\right)}^{-1}=\frac{\mathrm{adj} \left(\mathrm{adjA}\right)}{\left|\mathrm{adjA}\right|}$

         $$\begin{gathered} =\frac{|\mathrm{A}{|}^{\mathrm{n}-2}\mathrm{A}}{|\mathrm{A}{|}^{\mathrm{n}-1}} \\ =\frac{\mathrm{A}}{\left|\mathrm{A}\right|} \end{gathered}$$

         (2) is correct

(3)   $\det \left({\mathrm{A}}^{-1}\right)={\left(\det \mathrm{A}\right)}^{-1}$

        (3) is correct

(4)   $\mathrm{AdjA}=0$ if $\mathrm{A}=\mathrm{I}$

        $\mathrm{adjA}=\mathrm{I}$ is false