Let Da denote the group of motions of a square with vertices numerated in a clockwise...

 

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Let Da denote the group of motions of a square with vertices numerated in a clockwise way by the numbers 1, 2, 3, 4. a) Show that D4 is generated by the rotation R/2 (around the center of square) and by the reflection I over the line that goes through the vertices 1 and 3. b) Prove that RIR = 1. c) Prove that any element of D, has a form R'I, i = 0, 1, 2, 3. Let Da denote the group of motions of a square with vertices numerated in a clockwise way by the numbers 1, 2, 3, 4. a) Show that D4 is generated by the rotation R/2 (around the center of square) and by the reflection I over the line that goes through the vertices 1 and 3. b) Prove that RIR = 1. c) Prove that any element of D, has a form R'I, i = 0, 1, 2, 3.

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