Question: Take the square pattern covering the plane. Consider two symmetries. One flips the pattern about a diagonal line through the central square. The other rotates

Take the square pattern covering the plane. Consider two symmetries. One flips the pattern about a diagonal line through the central square. The other rotates the pattern 90 clockwise. If you first perform the flip and then the rotation, do you get the same symmetry as you would if you were to first do the rotation and then do the flip?

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