If $A = \begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix}$,then the determinant of the matrix $(A^{2016} - 2A^{2015} - A^{2014})$ is

If $A = \begin{bmatrix} 1 & 2 \\ -2 & -5 \end{bmatrix}$ and $\alpha A^2 + \beta A = 2I$ for some $\alpha, \beta \in \mathbb{R}$,then $\alpha + \beta =$

If $P = \begin{bmatrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \end{bmatrix}$,$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $Q = PAP^T$,then $P^T(Q^{2005})P$ is equal to

If $A = \begin{bmatrix} 0 & \sin \alpha \\ \sin \alpha & 0 \end{bmatrix}$ and $\det\left(A^{2} - \frac{1}{2} I\right) = 0$,then a possible value of $\alpha$ is

For $3 \times 3$ matrices $M$ and $N$,which of the following statement$(s)$ is (are) $NOT$ correct?

Let $d \in \mathbb{R}$,and $A = \begin{bmatrix} -2 & 4+d & \sin \theta - 2 \\ 1 & \sin \theta + 2 & d \\ 5 & 2\sin \theta - d & -\sin \theta + 2 + 2d \end{bmatrix}$,where $\theta \in [0, 2\pi]$. If the minimum value of $\det(A)$ is $8$,then a value of $d$ is