Determine the dimension of the following vector space and find a proper basis in which every matrix is of degree 1.

V = (see attachment)

If what I did is correct, the dimension is 2 and I found that these 2 matrices span V: (1, 0, 0, -3) (0, 1, -2, 0) (should be written properly as a 2x2 matrix, of course).

But now how can I find a basis where every matrix is of degree 1? How and why is it even possible to ensure such a thing? I simply find this incomprehensible for some reason.. I guess I'm missing something

Thanks!