If $A$ is a non-singular matrix such that $A \cdot A^T = A^T \cdot A$ and $B = A^{-1} \cdot A^T$,then

If $A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$,then $A^{-1}=$

Which of the following statements is/are incorrect?
$(i)$ Adjoint of a symmetric matrix is symmetric.
$(ii)$ Adjoint of a unit matrix is a unit matrix.
$(iii)$ $A(adj\,A) = (adj\,A)A = |A|I$.
$(iv)$ Adjoint of a diagonal matrix is a diagonal matrix.

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$,then $A(\operatorname{adj} A) = $

If $A = \begin{bmatrix} 1 & -3 & -5 \\ -2 & 4 & -6 \\ 7 & -11 & 13 \end{bmatrix}$,then $\sqrt{|\operatorname{Adj} A|} = $

If a matrix $A$ satisfies the equation $A^3-6A^2+11A-6I=0$,then $A^{-1}$ can be expressed in terms of $A$ as: