Show that if matrices A and B are elements of G, then AB is also an element of G. 
Let $G$ be the set of $2 \times 2$ matrices of the form
  \begin{pmatrix} a & b \\ 0 & c\end{pmatrix}
  such that $ac$ is not zero. Show that if matrices $A$ and $B$ are elements of $G$, then $AB$ is also an element of $G$.

Do I just need to show that $AB$ has a non-zero determinant? 

Another way to put it: entry $G_{21}$ is given by the dot product of vectors $(0 \space A_{22})$ and $(B_{11} \space 0)$. These are orthogonal, ie their dot product is zero, so that entry is always 0.
