If $A = \begin{bmatrix} 1 & \tan(\theta/2) \\ -\tan(\theta/2) & 1 \end{bmatrix}$ and $AB = I$,then $B = $

The inverse of the matrix $\begin{bmatrix} 5 & -2 \\ 3 & 1 \end{bmatrix}$ is

Let the matrix $A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix}$ and the matrix $B_{0} = A^{49} + 2A^{98}$. If $B_{n} = \text{Adj}(B_{n-1})$ for all $n \geq 1$,then $\det(B_{4})$ is equal to:

If $a, b, c$ and $d$ are real numbers such that $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+ib & c+id \\ -c+id & a-ib\end{array}\right]$,then $A^{-1}$ is equal to

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:

The inverse of the matrix $\left[ {\begin{array}{*{20}{c}}3&{ - 2}&{ - 1}\\{ - 4}&1&{ - 1}\\2&0&1\end{array}} \right]$ is