I'm stuck on the following and could use a hint.
Let $f:P\longrightarrow M$ be a map of finite dimensional modules over a finite dimensional algebra $A$ (over probably an algebraically closed field $K$), with $P$ projective. $f$ induces a map $\operatorname{top}f:\operatorname{top}P\longrightarrow \operatorname{top}M$ where $\operatorname{top}M = M/\operatorname{rad}M$ and $\operatorname{rad}M$ is the Jacobson radical.
Show that $\operatorname{top}f$ an isomorphism implies $f:P\longrightarrow M$ is a projective cover.
Don't really know where to start.