How to calculate below permutation
(2 3)I(3 2)
To calculate the permutation (2 3)I(3 2), we need to understand the concept of composition of permutations. Composition of permutations involves performing one permutation and then another permutation on the resulting arrangement.
In this case, we have two permutations - (2 3) and (3 2). The first permutation (2 3) swaps the positions of 2 and 3. The second permutation (3 2) then swaps the positions of 3 and 2 back to their original positions.
When we compose these two permutations, we get the identity permutation I, which means that all elements in the permutation are in their original positions.
Therefore, (2 3)I(3 2) = I.
To calculate the permutation (2 3)I(3 2), follow these steps:
Step 1: Start with the identity permutation.
I: [1, 2, 3]
Step 2: Apply the permutation (3 2) to the current permutation.
I(3 2): [1, 3, 2]
Step 3: Apply the permutation (2 3) to the current permutation.
(2 3)I(3 2): [2, 1, 3]
Therefore, the result of the permutation (2 3)I(3 2) is [2, 1, 3].