Let $\theta = {\pi \over 5}$ and $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$. If B = A + A4 , then det (B) :

Question

Let $\theta = {\pi \over 5}$ and $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$.

If B = A + A⁴ , then det (B) :

lies in (1, 2)