Let's see how far we can go:
$M=\left[\begin{array}{cccc}{\alpha}_{1}& {\alpha}_{1}^{q}& \dots & {\alpha}_{1}^{{q}^{n-1}}\\ {\alpha}_{2}& {\alpha}_{2}^{q}& \dots & {\alpha}_{2}^{{q}^{n-1}}\\ \vdots & \vdots & \ddots & \vdots \\ {\alpha}_{m}& {\alpha}_{m}^{q}& \dots & {\alpha}_{m}^{{q}^{n-1}}\end{array}\right]$
👁️