Describe the action of r^-1 on the square and express r^-1 as a word using r only

Question

It says let r be the element of R4 that rotates the square by 90 degrees clockwise

What I did was make a square and I turned it 90 degrees. So would the inverse of the 90 degree square be the counter clockwise

Answer 1

Yes, the inverse of a 90 degree rotation clockwise is a 90 degree rotation counterclockwise. The question you are being asked however is how you express that in terms of $r$ i.e. how do you express a 90 degree rotation counterclockwise in terms of 90 degree rotations clockwise.

A hint is to consider what happens if you take powers of $r$, i.e. what happens if you rotate 90 degrees clockwise multiple times.