Adjoint of a Matrix

Let for $A=\left[\begin{array}{lll}1& 2& 3\\ \alpha & 3& 1\\ 1& 1& 2\end{array}\right],\left|A\right|=2$. If $|2adj(2adj\left(2A\right)\left)\right|={32}^n$, then $3n+\alpha$ is equal to

If $A=\frac{1}{5!6!7!}\left[\begin{array}{lll}5!& 6!& 7!\\ 6!& 7!& 8!\\ 7!& 8!& 9!\end{array}\right]$, then $\left|adj\left(adj\left(2A\right)\right)\right|$  is equal to

Let $B=\left[\begin{array}{lll}1& 3& \alpha \\ 1& 2& 3\\ \alpha & \alpha & 4\end{array}\right],\alpha >2$ be the adjoint of a matrix $A$ and $\left|A\right|=2.$ Then $\left[\begin{array}{ccc}\alpha & -2\alpha & \alpha \end{array}\right]B\left[\begin{array}{c}\alpha \\ -2\alpha \\ \alpha \end{array}\right]$ is equal to

Let the determinant of a square matrix $A$ of order $m$ be $m-n$, where m and $n$ satisfy $4m+n=22$ and $17m+4n=93$. If $det\left(n adj\left(adj\left(mA\right)\right)\right)=3^a{5}^b{6}^c$, then $a+b+c$ is equal to

If $A$ is a $3\times 3$ matrix and $\left|A\right|=2$, then $\left|3\mathit{adj}\left(\left|3A\right|A^2\right)\right|$ is equal to

Let $\left[\begin{array}{ccc}\begin{array}{c}2\\ 1\\ 0\end{array}& \begin{array}{c}1\\ 2\\ -1\end{array}& \begin{array}{c}0\\ -1\\ 2\end{array}\end{array}\right]$. If $\left|adj(adj\left(adj2A)\right)\right|=(16{)}^n$, then $n$ is equal to

Matrix $A$ having order $m$ has the value of its determinant as $m^{-n}$. The value of $\text{det}\left(nadj\left(adj\left(mA\right)\right)\right)$ is

If matrix $A=\left[\begin{array}{ccc}1& 2& 1\\ \alpha & 3& 2\\ 3& 1& 1\end{array}\right]$ and $\left|A\right|=2$ then value of $\left|\alpha adj\left(\alpha adj\left(\alpha A\right)\right)\right|$ is

If the order of the matrix $A$ is $3\times 3$ and $\left|A\right|=2$, then the value of $\left|3adj\left(\left|3A\right|A^2\right)\right|$ is 

If $A=\left[\begin{array}{ccc}2& 1& 0\\ 1& 2& -1\\ 0& 1& 2\end{array}\right]$ and $\left|adj\left(adj\left(adjA\right)\right)\right|={16}^n$ then the value of $n$ is

If $A$ is a square matrix of order $\left(3\times 3\right)$ such that $\left|A\right|=2$, then $\mathrm{adj}\left(\mathrm{adj}A\right)$ is 

Given $A=\left[\begin{array}{ccc}a& 2& 2\\ 1& b& 4\\ 3& 5& c\end{array}\right]$, where $abc=-10$ and $10a+3c+c=17$. Value of $\left|A.Adj\left(A\right)\right|$ will be

Let $S=\left\{\sqrt{n}+1; 1\le n\le 40 \mathrm{and} n i\mathrm{s} \mathrm{odd}\right\}$. Let $a\in S$ and $A=\left[\begin{array}{ccc}1& 0& a-1\\ -1& 1& 0\\ -a+1& 0& 0\end{array}\right]$. If $\sum _{a\in S}\det \left(\mathrm{adj}A\right)=41\mathrm{\lambda }$, then $\lambda$ is equal to

If $A$ is a square matrix of order $3$ then $\left|\mathrm{Adj}\left(\mathrm{Adj}{A}^2\right)\right|=$

If $A=\left[\begin{array}{ccc}-1& 1& 1\\ 1& -1& 1\\ 1& 1& -1\end{array}\right]$, then which one of the following is correct

If $A={\left[a_{ij}\right]}_{3\times 3}$, such that $a_{ij}=\left\{\begin{array}{l}2, \mathrm{when} i=j\\ 0, \mathrm{when} i\ne j\end{array}\right.$, then $1+{\log }_{1/2}det(Adj\left(Adj\left(A\right)\right)=$

For a matrix $A$, if $\left|A\right|=6$ and $\left(\mathrm{adj}\right)A=\left[\begin{array}{ccc}1& -2& 4\\ 4& 1& 1\\ -1& k& 0\end{array}\right]$, then $k$ is equal to

If $A=\left[\begin{array}{ccc}2& 52& 152\\ 4& 106& 358\\ 6& 162& 620\end{array}\right]$, then the determinant of the matrix $\mathrm{adj}\left(2A\right)$ is equal to

Let $A$ be a matrix of order $3\times 3$ such that $\det \left(\mathrm{A}\right)=2,B=2A^{-1}$ and $C=\frac{\left(\mathrm{adjA}\right)}{\sqrt[3]{16}}$ , then the value of $\det \left(A^3{B}^2{C}^3\right)$ is

$A$ is a $3\times 3$ matrix with real entries, such that $A^{-1}=adj\left(adj\left(A\right)\right)$, then which of the following is incorrect, where$I$ is $3\times 3$ identity matrix?