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Let A be a finite set. If f: AvecA is an...

Let A be a finite set. If `f: AvecA` is an onto function, show that `f` is one-one also.

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Given that `f:A->A` is an onto function.
Let `A->{a_1,a_2,a_3....a_n}`
As this is an onto function from `A->A`,
`:. f(A) ->{f(a_1),f(a_2),f(a_2)...f(a_n)} = A`
It means, `f(a_1),f(a_2)...f(a_n)` are all distinct elements of `A`.
`:. f: A->A` is one-one function.
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