(p). [(1 2 3 5) (4 6 7 ) ]^(-1) Solve [(1 2 3 5) (4 6 7 )]^(-1) Step1: Compute The product [(1 2 3 5) (4 6 7 ) ]^(-1) We apply permutation from right to left. Let's track what happens to each element (1,2,3,4,5,6,7): Apply (4 6 7) first: 46 67 74 1,2,3,5 unchanged Apply (1 2 3 5) 12 23 35 51 4,6,7 unchanged Let's follow each number Start with 1 (4 6 7):11 (1 2 3 5):12 So, 12 Start with 2: (4 6 7):22 (1 2 3 5):23 So, 23 Start with 3: (4 6 7):22 (1 2 3 5):23 So, 23 Start with 4: (4 6 7):46 (1 2 3 5):66 So, 46 Start with 5: (4 6 7):55 (1 2 3 5):51 So, 51 Start with 6: (4 6 7):67 (1 2 3 5):77 So, 67 Start with 7: (4 6 7):74 (1 2 3 5):44 So, 74 Thus, the permutation is 12351 4674 This is the cycle (1 2 3 5)(4 6 7) Step2. Find the Inverse The inverse of (1 2 3 5)(467) is (5 3 2 1)(7 6 4) Therefore, the solution is ([(1 2 3 5) (4 6 7 ) ]^(-1)=(5 3 2 1)(7 6 4) check this plese for me