# Bilinear Maps and their relationships with dual bases

I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.

Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,

f is dual bilinear maps iff M(f,T,S) is regular matrix.

(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)