Although the determinate of that matrix = 0, and if it's conjugate transpose determinant is non zero then I wonder if all valid possible configurations on this

Although the determinate of that matrix = 0, and if it's conjugate transpose determinant is non zero then I wonder if all valid possible configurations on this board can be represented by a complex lie group? Edit: did the work, it does, but too lazy to describe the group https://gist.github.com/cinquemb/18e494348045725e2b60 https://gist.github.com/cinquemb/18e494348045725e2b60