Let V be the vector space Mn×n(R), and let B: V×V→R be the bilinear form B(X, Y) = tr(XY). Calculate the signature of B. Here, tr means the trace of the matrix. Edits
I'm stuck here as I was only able to conclude that this is a symmetric bilinear form (correct me if I'm wrong), then how to proceed after this? I am having no idea on how to proceed on this question.