Write down the six elements of S3 and give the multiplication table for the group. The six elements of S3 are then: 1 2 1 3 1 = (1 ²23). a = (²2 ²3). b = (²²2) 1 3 1 1 c = (2²²3). α = (²2²3). == (1 3²2) 1 The multiplication table for S3 can be written down directly by doing the required composition. Find ab, de,and c^2 2 3 2 3 2 3 2 3 a = ( ²2 ²3 ³) a = ( ²2 ²3 ³)=b (² ² 2) ² = ( 2² ²³) a= 1 1 3 1 a3 = (₁ 2²3) = 1 1 2 2 2 c = ( ₂2 ²3 ) c = ( ₂2 ² 3) = c ² = c = (₁ ²₂3) ²¹ C 1 1 2

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