The adjoint of the matrix $N = \begin{bmatrix} -4 & -3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \end{bmatrix}$ is

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 $A$ and $B$ are non-singular matrices of the same order,then $\text{Adj}(AB)$ is:

If $A = \begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix}$,then $A^{-1}$ is

Find the inverse,by elementary row operations (if possible),of the following matrix: $\left[\begin{array}{cc}1 & 3 \\ -5 & 7\end{array}\right]$

If $A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4\end{array}\right]$ and $\operatorname{adj} A=\left[\begin{array}{ccc}4 & -1 & 1 \\ 8 & -7 & a \\ 9 & -6 & b\end{array}\right]$,then find the values of $a$ and $b$.