liniær algebra

Hej. Jeg har problemer med de her to spørgsmål. Jeg håber nogle kan hjælpe:

V is a vector space of nxn matricer. For A,B∈V:

(A,B) = tr(AB);

1) Let W be the subspace of matrix A such that tr(A) = 0. What is the
dimension of the orthogonal complement W^⊥, relative to the inner product ( , )?
2)Give an explicit basis for W^⊥