2) Solve a) R180 o D o R270 =

b) R90 o V o H =

c) V o O o H =

d) I o H o I =

In the case of d) use the associative property (from the notes) to prove your solution.

e) From table 1, you could see that D o D = I, V o V = I, H o H = I, and O o O = I. Same for R180 o R180 = I. Could you explain why all of them are equal to I (the identity element)?

f) From the notes, you learn that a o b = b o a = I, then b is the inverse of a.

Following your explanation of e), could you explain how is possible that the inverse element is the same in the case of D, V, H, O, and R180?