I have a question, suppose that T is a linear transformation and M_B_Bc(T) if the matrix of T relative to basis B and canonic basis Bc. Knowing B and Bc, how can i get T?
A more explicit example would be something like:

B=((1,2),(1,1)) and Bc=((1,0),(0,1)) and T a linear transformation.
M_B_Bc(T) = [[3,2],[2,1]] where [3,2]and [2,1] are columns of the matrix.

What is the procedure to get T?