If $A$ and $B$ are non-singular matrices,then which of the following is true?

The multiplicative inverse of $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ is

${\left[ {\begin{array}{*{20}{c}}1&3\\3&{10}\end{array}} \right]^{ - 1}} = $

If matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}$ and $A^{-1} = \alpha I + \beta A$ where $I$ is a unit matrix of order $2$ and $\alpha, \beta$ are constants,then the value of $\alpha + \beta + \alpha \beta$ is

The inverse of the matrix $A = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{bmatrix}$ is

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