If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{-1} = I$,then $\alpha =$

Find the adjoint of the matrix $A = \left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right]$.

If $A$ is a $3 \times 3$ matrix such that $|5 \times \text{adj} A|=5$,then $|A|$ is equal to

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

If $A$ is an invertible matrix of order $n$, then the determinant of $\operatorname{adj} A$ is equal to :

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: