If $A$ is a square matrix of order $3 \times 3$ and $\operatorname{det}(A) = 3$,then the value of $\operatorname{det}(3A^{-1})$ is:

If $A=\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}$ and $B=\begin{bmatrix} 4 & 1 \\ 3 & 1 \end{bmatrix}$,then $(A+B)^{-1} = $

If $Q$ is the inverse of $A$,where $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10Q = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & x \\ 1 & -2 & 3 \end{bmatrix}$,find $x$.

Find the inverse,by elementary row operations (if possible),of the following matrix: $\left[\begin{array}{cc}1 & -3 \\ -2 & 6\end{array}\right]$

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$ and $A(\operatorname{adj} A) = kI$,then the value of $(k+1)^4$ is

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: