Let $\theta=\frac{\pi}{5}$ and $A=\left[\begin{array}{cc}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{array}\right]$. If $B=A+A^{4}$, then $\det(B)$: (1) is one (2) lies in $(2,3)$ (3) is zero (4) lies in $(1,2)$
Let $\theta=\frac{\pi}{5}$ and $A=\left[\begin{array}{cc}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{array}\right]$. If $B=A+A^{4}$, then $\det(B)$:\\
(1) is one\\
(2) lies in $(2,3)$\\
(3) is zero\\
(4) lies in $(1,2)$