If $A=\left[\begin{array}{lll}a& 0& 0\\ 0& a& 0\\ 0& 0& a\end{array}\right]$, then value of $\left|adj(adj(adjA\left)\right)\right|\left|adj\left(A^{-1}\right)\right|=a^{\lambda }$ then $\lambda$ is equal to

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 .