If $A$ is a matrix of order $3$ whose determinant is equal to $6$,then $\operatorname{det}(\operatorname{adj} A) = $

$Adj(AB) - (Adj B)(Adj A) = $

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a matrix $A$ and $\det(A) = 4$,then the value of $\alpha$ is

If $A$ is a non-zero square matrix of order $n$ with $\det(I+A) \neq 0$ and $A^3=O$, where $I$ and $O$ are the identity and null matrices of order $n \times n$ respectively, then $(I+A)^{-1}$ is equal to

If $A$ and $B$ are non-singular matrices of order $2$ such that $(AB)^{-1} = \frac{1}{6} \begin{bmatrix} -7 & -3 \\ 2 & 3 \end{bmatrix}$ and $A^{-1} = \frac{1}{3} \begin{bmatrix} 4 & 3 \\ -1 & 0 \end{bmatrix}$,then $B^{-1} = $

Let $A$ be a $3 \times 3$ matrix and $B$ be its adjoint matrix. If $|B|=64,$ then $|A|$ is equal to