Matrices And Determinants

For \(\alpha, \beta \in \mathbb{R}\) and a natural number \(n\), let $$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}+\alpha \\ 2 r & 2 & n^2-\beta \\ 3 r-2 & 3 & \frac{n(3 n-1)}{2}\end{array}\right|$$. Then \(2 A_{10}-A_8\) is