Consider a injective function f: A --> A
A being a finite Set.
Lets assume that the function f is not Surjective:
Therefore the equality f(x)≠y does not holds for some 'y' .
But
since each element of A must be mapped to an element of A, if there were an element y such that
there doesn’t exist an element x in A such that f(x) = y, then one element of A must be mapped to
two elements for the function f to exist.
Elements of A must be mapped to elements of A.But if f(x)≠y ,then for a function to be valid one element maps to 2 elements which is not possible in case of injective function.
Therefore if f:A--> is Injective then it is also Surjective.
Hence Proved!