Question

The set of all bijective functions from a finite set A to itself forms:

Q: Answer-The set of all bijective functions from a finite set A to itself forms:

The set of all bijective functions i.e., permutations from a finite set A to itself is known as the symmetric group on A, commonly denoted S if A has n elements. This set forms a group under function composition because Closure Composition of two bijections is a bijection. Associativity Function composition is associative. Identity element The identity function maps every element to itself is a bijection and acts as the identity. Inverses Every bijective function has an inverse, which is also a bijection. Hence, this structure satisfies all group axioms.