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Can you help me to compute determinant of matrix

$$A =\begin{pmatrix} 5 &3 &0 &\cdots &0 &0 \\ 2&5 &3 &\cdots &0 &0 \\ 0&2 &5 &\cdots & 0 &0 \\ \cdots & \cdots &\cdots & \cdots &\cdots &\cdots \\ 0&0 &0 &\cdots &\cdots &3 \\ 0& 0& 0& \cdots & 2 &5 \end{pmatrix}$$

and dimension of $A$ is $n \times n$.

I don't know how to solve it !

joriki
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