linear algebra - Proof on Endomorphism

Let A be element of Endomorphism of V (V is a finite dimensional vector space over F) such that A is onto.
Assume that there exist a function
B: V $\to$ V such that BA = I. Prove that AB = I

• Can you give me a hint on how to prove this problem? Thanks.

Here is working solution. Since A is onto, there exist x in V such that A(x) = v.

We need to show that BA = I.

(BA)(x) = B(A(x)) = B(v) then I don't know what's next