Q: Is it possible to do symbolic vector or matrix manipulations in Mathematica?
Answer
Yes. For example:
In[1]:= matrix = {{a, b}, {c, d}}; In[2]:= Inverse[matrix]//TraditionalForm Out[2]//TraditionalForm= ( d b ) --------- ---------- a d - b c a d - b c c a ---------- --------- a d - b c a d - b c