Geogebra model for hyperbolic isometries

The goals of this GeoGebra model are the following:

1) Input a hyperbolic isometry of the hyperbolic plane using the matrix representation. In other words input a real matrix with determinant 1 and trace more than 2.

2) Programmatically draw the axis.

3) Mark any point P on the hyperbolic plane (upper half plane)

4) Show the movement of the point P when powers of the isometry are applied sequentially

Here is a little video demonstration

Here is the Geogebra worksheet:

https://www.geogebra.org/m/rvnkn7pu