I want to know the answer to the following question:
What is a finite composition of two symmetries or their inverses?
All the background I'm provided with is that "The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses.". Is that enough to answer the question?
Answer: yes