Let $A = \begin{bmatrix} -3 & 2 \\ 1 & 4 \end{bmatrix}$ and if $A^2 - 2A + I = \begin{bmatrix} 18 & p \\ q & 11 \end{bmatrix}$, then $\ldots$

Let $A = \begin{bmatrix} \cos\alpha & -\sin\alpha & 0 \\ \sin\alpha & \cos\alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$. If $B = \text{adj}\,A$, then the matrix $B^{-1}$ is equal to...

Let $A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 6 & -13 \\ 5 & -10 \end{bmatrix}$ be two matrices. If the variables $x$ and $y$ satisfy the matrix equation $((A^{-1})^2 + B)\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}$, then the ordered pair $(x, y) = $

If $A = \begin{bmatrix} 1 & -\tan\dfrac{\theta}{2} \\ \tan\dfrac{\theta}{2} & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & \tan\dfrac{\theta}{2} \\ -\tan\dfrac{\theta}{2} & 1 \end{bmatrix}$ then $A^{-1}B$ is equal to