(o). [(1 2) (3 4) ( 1 2) ( 4 7)]^(-1) Solve [(1 2) (3 4) ( 1 2) ( 4 7)]^(-1) Step1: Compute The product (1 2) (3 4) ( 1 2) ( 4 7) We apply permutation from right to left. Let's track what happens to each element (1,2,3,4,7): Apply (4 7) first: 47 74 1,2,3 unchanged Apply (1 2) 12 3,4,7 unchange Apply(3 4) 34 1,2,7 unchange Apply(1 2) 12 3,4,7 unchange Let's follow each number Start with 1 (4 7):11 (1 2):12 (3 4):22 (1 2):21 So, 11 Start with 2: (4 7):22 (1 2):21 (3 4):11 (1 2):12 So, 22 Start with 3: (4 7):33 (1 2):33 (3 4):34 (1 2):44 So, 34 Start with 4: (4 7):74 (1 2):44 (3 4):43 (1 2):33 So, 73 Thus, the permutation is 3473 This is the cycle (3 4 7) Step2. Find the Inverse The inverse of (3 4 7) is (7 4 3) Therefore, the solution is [(1 2) (3 4) ( 1 2) ( 4 7)]^(-1)= (7 4 3) check this out plese