how to prove: If A and B are finite sets with the same number of elements, then f: A --> B is bijective iff f is injective iff f is surjective.
That is a bit confused I think. Because a function is bijective iff it is both injective and surjective. So that is by definition.
Now if then any function from A to B is injective if and only if it is also surjective.
I will help you one way. Suppose that is bijective.
From subjectivity, .
From injectivity, .
Therefore .