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Math Help - Commutative Diagram of Modules

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    Commutative Diagram of Modules

    Let A be a ring. The following is a commutative diagram of A-module homomorphisms, and the rows are exact.



    Suppose that f_1 is surjective and that f_2 is an isomorphism. Prove that f_3 is an isomorphism.

    Attempt
    Onto- f_3 = t \circ f_2 and both f_2 and t are both onto so t \circ f_2 is onto.
    1-1- This one doesn't seem as trivial. I am a bit confused on showing this.

    Thanks in advance for any hints.
    Last edited by xianghu21; May 15th 2009 at 07:28 AM.
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