A free program for Android, by STEMath.
The GaussElim app is an interactive tool that can be used to calculate the inverse and the null space of a given matrix. You can easily set the matrix dimensions and then you can edit the matrix elements by typing in each cell. You can use the scroll bars to move from one cell to the next and you can tap the desired cell to change its contents. The calculation process is quite simple and you can see the results on the bottom of the screen.
If you want to learn more about this tool, you can download it from the Google Play Store.