Exercise 4, § 2

Give an example of a bijective $A$-linear mapping $u : E \to F$, where $E$ and $F$ are two filtered $A$-modules, such that $u$ is compatible with the filtrations but $\operatorname{gr}(u)$ is neither injective nor surjective. (Take $E = A, F = A$ with another filtration and $u$ the identity mapping.)