Question

If σ is an even permutation, then σ ² = I . Write given statement is true or false, justify your answer.

Answer 1

This statement is false. Example:
Let {1, 3, 4, 2} be the even permutation of four elements. Then, ( {1, 3, 4, 2})( {1, 3, 4, 2}) = ({1,4}{3, 2}), that is not equal to 1.