Suppose

is a commutative diagram of modules over some ring . Suppose the rows are exact and and are bijective. Prove is bijective.

Attempt:

I know the snake lemma and five lemma. This looks more like a diagram chasing question. In the five lemma and snake lemma I can use the commutativity of the diagram, but here, is on the left, so I don't know how to use the commutativity of the diagram. Any hints for showing this would be nice. Thanks.