If $A$ is a singular matrix, then $adj A$ is

Which of the following is/are true?

(i) Adjoint of a symmetric matrix is symmetric 

(ii) Adjoint of a unit matrix is a unit matrix  

(iii) $A\left(adjA\right)=\left(adjA\right)A=\left|A\right|I$ and 

(iv) Adjoint of a diagonal matrix is a diagonal matrix .