Adjoint and Inverse of a Matrix

Let $A, B, C$ be three $4\times 4$ matrices such that $detA=5,detB=-3$, and $detC=\frac{1}{2}.$ Then the $det\left(2A{B}^{-1}{C}^3{B}^T\right)$ is

Let $P$ be a matrix of order $3\times 3$ and $det\left(P\right)=3$, then the value of $det\left(adj\left(adj P\right)\right)$ is

For any $2\times 2$ matrix, if $A\left(adj A\right)=\left[\begin{array}{cc}20& 0\\ 0& 20\end{array}\right]$, then $\left|A\right|$ equals

If $Q$ is a non-singular matrix, then the value of $adj\left(Q^{-1}\right)$ in terms of $Q$ is

If the value of a third order determinant is $10$, then the value of the square of the determinant formed by its cofactors will be

If $A=\left[\begin{array}{lll}1& 2& 3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right] \text{and} BA=A$, where $B$ represent $3\times 3$ order matrix. If total number of $1$'s in matrix $A^{-1}$ and matrix $B$ are $p$ and $q$ respectively, then the value of $p^2+q^2$ is

If $A=\left[\begin{array}{cc}-2& 4\\ 1& -3\end{array}\right]$, then $A^{-1}=$.

If $A=\left[\begin{array}{l}2\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}4\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}1\\ 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}7\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\end{array}\right]$, then $adj\left(A\right)=$

If $A=\left[\begin{array}{rrr}3& -3& 4\\ 2& -3& 4\\ 0& -1& 1\end{array}\right]$, then $adj\left(\mathrm{adj}A\right)$ is

If $P=\left[\begin{array}{lll}1& x& 0\\ 1& 3& 0\\ 2& 4& -2\end{array}\right]$ is the adjoint of $3\times 3$ matrix $A$ and $\left|A\right|=4,$ then $x$ is

If $A=\left[\begin{array}{ll}2& 0\\ 1& 5\end{array}\right]$ and $B=\left[\begin{array}{ll}1& 4\\ 2& 0\end{array}\right]$, then $\left|\mathrm{adj}\left(AB\right)\right|=$

If $A=\left[\begin{array}{ll}7& 3\\ 4& 2\end{array}\right]$, then $9I_2-A=$

If $A=\left[\begin{array}{ll}3& 5\\ 1& 2\end{array}\right], B=adjA$ and $C=3A$, then $\frac{|adjB|}{\left|C\right|}=$

If $|adj(adj\mathrm{A}\left)\right|=|\mathrm{A}{|}^9,$ then the order of the square matrix is

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

If the value of a third order determinant is $12$, then the value of the determinant formed by replacing each element by its co-factor will be 

The adjoint of the matrix $A=\left[\begin{array}{cc}2& -3\\ 3& 5\end{array}\right]$ is

If $A=\left[\begin{array}{ccc}\frac{k}{2}& 0& 0\\ 0& \frac{l}{3}& 0\\ 0& 0& \frac{m}{4}\end{array}\right]$ and $A^{-1}=\left[\begin{array}{ccc}\frac{1}{2}& 0& 0\\ 0& \frac{1}{3}& 0\\ 0& 0& \frac{1}{4}\end{array}\right]$ then $k+l+m=$