Question: Given an equilateral triangle, six permutations can be performed on the triangle that will leave its image in the plane unchanged. Three of these permutations are clockwise rotations in the plane of 120°, 240°, and 360° about the center of the triangle; these permutations are denoted R1, R2, and R3, respectively. The triangle can also be flipped about any of the axes 1, 2, and 3 (see the accompanying figure); these permutations are denoted F1, F2, and F3, respectively. During any of these permutations, the axes remain fixed in the plane. Composition of permutations is a binary operation on the set D3 of all six permutations. For example, F3 + R2 = F2. The set D3 under composition is a group, called the group of symmetries of an equilateral triangle. Complete the group table below for 3D3, +4. What is an identity element in 3D3, +4? What is an inverse element for F1? For R2
