Another question I dont get - I need to show that D & E are isomorphic
What is a possible basis for $\displaystyle D$?
Let $\displaystyle M = \left[{\begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}}\right]$ where $\displaystyle a,b,...,i \in \mathbb{Z}$
compute for $\displaystyle TM$. That $\displaystyle TM$ is in $\displaystyle E$.
based on $\displaystyle TM$, what is a possible basis for $\displaystyle E$.
if number of basis elements of D = number of basis elements of E, then you are done..