# Intriguing Determinant

Geometry Level 5

Let $$A_n=(a_{ij})$$ be the $$n\times n$$ matrix with $$a_{ii}=2\cos\left(\dfrac\pi{180}\right)$$ , $$a_{ij}=1$$ if $$|i-j|=1$$ and $$a_{ij}=0$$ otherwise, for all $$n$$. Find the maximal value of $$\det(A_n)$$, for all positive integers $$n$$.

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