I'm not completely sure whether the question is clear enough to me, but I can think of the following: if the matrix has two eigenvalues , then is similar to the matrix , and since we know that , and this last one has a very nice and simple geometric interpretation we get (?) what we want: it is the "volume" (generalized algebraic volume, which in this case is 2-dimensional volume = usual area) of the parallelogram (rectangle in this case) generated by the 2-dimensional vectors

Tonio