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

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

If $\begin{bmatrix} 1 & -\tan \theta \\ \tan \theta & 1 \end{bmatrix} \begin{bmatrix} 1 & \tan \theta \\ -\tan \theta & 1 \end{bmatrix}^{-1} = \begin{bmatrix} a & -b \\ b & a \end{bmatrix}$,then

Using elementary transformations,find the inverse of the following matrix,if it exists: $A = \begin{bmatrix} -1 & 2 \\ -3 & 5 \end{bmatrix}$

Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $\det(A)=-4$ and $A+I=\begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix}$,where $I$ is the identity matrix of order $3 \times 3$. If $\det((a+1) \operatorname{adj}((a-1) A)) = 2^m 3^n$,where $m, n \in \{0, 1, 2, \ldots, 20\}$,then $m+n$ 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 $\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(mA))) = 3^a 5^b 6^c$,then $a + b + c$ is equal to: