In page 60 of Hall's textbook, ex. 8 assignment (c), he asks me to prove that if $A$ is a unipotent matrix then $\exp(\log A))=A$.
In the hint he gives to show that for $A(t)=I+t(A-I)$ we get
$$\exp(\log A(t)) = A(t) , \ t<<1$$
I don't see how I can plug here $t=1$, this equality is true only for $t \rightarrow 0$, right?