The row operation matrix inversion method is so neat and ingenious, and it has the same operations for all dimensions of matrix.
Here is a step by step approach, where firstly the dimension is chosen, then the first of the buttons is selected (Start). After which the buttons are selected in order. The states of the left and right matrices are displayed at each stage, and finally the identity matrix appears on the left, and the inverse of the original matrix appears on the right.
The first display shows the original matrix on the left. Nothing has been done yet.
The second one is the 2 x 2 matrix inverted.
The third is the 4 x 4 matrix inverted.