If $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$,then $A^{-1}$ is given by

Let $A$ be a $n \times n$ matrix such that $|A|=2$. If the determinant of the matrix $\operatorname{Adj}(2 \cdot \operatorname{Adj}(2A^{-1}))$ is $2^{84}$,then $n$ is equal to:

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, $C = \begin{bmatrix} 7 & 3 \\ 0 & 6 \end{bmatrix}$ and $AB = C$, then the inverse of matrix $B$ is

Let $A = \begin{bmatrix} 1 & 2 \\ -1 & 4 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$,where $\alpha, \beta \in \mathbb{R}$ and $I$ is a $2 \times 2$ identity matrix,then $4(\alpha - \beta)$ is equal to:

If the inverse of $\begin{bmatrix} 1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6 \end{bmatrix}$ does not exist,then $x=$

Find the inverse of the matrix $A = \left[\begin{array}{cc}2 & -3 \\ -1 & 2\end{array}\right]$,if it exists.