Определитель произведения матриц

$\left[\begin{smallmatrix} \cos \left(\alpha_{1}-\beta_{1}\right) & \cos \left(\alpha_{1}-\beta_{2}\right) & \ldots & \cos \left(\alpha_{1}-\beta_{n}\right) \\ \cos \left(\alpha_{2}-\beta_{1}\right) & \cos \left(\alpha_{2}-\beta_{2}\right) & \ldots & \cos \left(\alpha_{2}-\beta_{n}\right) \\ \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots & \ldots \ldots & \ldots \ldots \\ \cos \left(\alpha_{n}-\beta_{1}\right) & \cos \left(\alpha_{n}-\beta_{2}\right) & \ldots & \cos \left(\alpha_{n}-\beta_{n}\right)\end{smallmatrix}\right] ;$

$\left[\begin{smallmatrix} \frac{1-a_{1}^{n} b_{1}^{n}}{1-a_{1} b_{1}} & \ldots & \frac{1-a_{1}^{n} b_{n}^{n}}{1-a_{1} b_{n}} \\ \vdots & \ddots & \vdots \\ \frac{1-a_{n}^{n} b_{1}^{n}}{1-a_{n} b_{1}} & \ldots & \frac{1-a_{n}^{n} b_{n}^{n}}{1-a_{n} b_{n}}\end{smallmatrix}\right]$;

$\left[\begin{smallmatrix} \left(a_{0}+b_{0}\right)^{n} & \ldots & \left(a_{0}+b_{n}\right)^{n} \\ \vdots & \ddots & \vdots \\ \left(a_{n}+b_{0}\right)^{n} & \ldots & \left(a_{n}+b_{n}\right)^{n}\end{smallmatrix}\right]$;

$\left[\begin{smallmatrix} s_{0} & s_{1} & s_{2} & \ldots & s_{n-1} \\ s_{1} & s_{2} & s_{3} & \ldots & s_{n} \\ s_{2} & s_{3} & s_{4} & \ldots & s_{n+1} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ s_{n-1} & s_{n} & s_{n+1} & \ldots & s_{2 n-2}\end{smallmatrix}\right], \quad$ где $\quad s_{k}=x_{1}^{k}+x_{2}^{k}+\ldots +x_{n}^{k}$.

$\left|\begin{array}{llll}a & b & c & d \\ d & a & b & c \\ c & d & a & b \\ b & c & d & a\end{array}\right| ; \quad$

$\left[\begin{smallmatrix} 1 & \alpha & \alpha^{2} & \ldots & \alpha^{n-1} \\ \alpha^{n-1} & 1 & \alpha & \ldots & \alpha^{n-2} \\ \alpha^{n-2} & \alpha^{n-1} & 1 & \ldots & \alpha^{n-3} \\ \ldots \ldots & \ldots \ldots & \ldots & \ldots & \ldots \\ \alpha & \alpha^{2} & \alpha^{3} & \ldots & 1\end{smallmatrix}\right]$.