Suppose

is a commutative diagram of modules over some ring $\displaystyle R$. Suppose the rows are exact and $\displaystyle g$ and $\displaystyle h$ are bijective. Prove $\displaystyle f$ 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, $\displaystyle f$ 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.