Problem: Show that $D_n$ is a group with composition, where order of $D_n$ is $2n$ and $$D_n=\{e,a,...,a^{n-1},b,ab,...,a^{n-1}b\}$$with the following relations: $a^n=e$, $b^2=e$, $ba=a^{n-1}b$.
Closure: Let $x,y\in D_n$. Then $x=a^{j_1}b^{k_1}$ and $y=a^{j_2}b^{k_2}$ for some $j_1,k_1,j_2,k_2\in\mathbb{Z}$. I want to show that $x\circ y\in D_n$. I don't really understand how to do this. Kindly help me!