Since $a=\frac{1}{n}$ where $n$ is a positive integer with $n>1$, then $0<a<1$ and $\frac{1}{a}=n>1$. Thus, $0<a<1<\frac{1}{a}$, which eliminates choices (D) and (E). Since $0<a<1$, then $a^{2}$ is positive and $a^{2}<a$, which eliminates choices (A) and (C). Thus, $0<a^{2}<a<1<\frac{1}{a}$, which tells us that (B) must be correct.