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GO Classes DPP | GATE CS | Discrete Mathematics| Group Theory

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Abelian Group : The Group which satisfy commutative properties ( a op b = b op a )

Option A: Group of all Permutations of a set is not Commutative, Because in Permuation order matters

      Eample: {1,2,3}

  • If we first swap 1 and 2 and then 2 and 3 we get {3,1,2}
  • If we first swap 2 and 3 and then 1 and 2 we get {2,3,1}          

Thus, order matters in permutations        

Option B: Multiplication of two Matrices is not Commutative

Option C: Group of all 3D rotations is not Commutative because Order of rotation Matters.

              Example: Rotating Clokwise 60° then Anticlockwise 30° is different from Rotating AntiClokwise 60° then Clockwise 30°

Option D: Group of all Integers Under addition is commutative because addition is commutative

                         a+b = b+a

Hence, Option D

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