T:V -> V is linear. V is finite vectorspace of dimension m^2. T(M) = AMB where M is an mXm matrix and A, B are two fixed mXm matrices. I want to find the trace and determinant of this transformation. In the case where B is the indentity, I can show that the trace is m*tr(A) and the determinant is m*det(A). This is so because the matrix of this linear map can be written as an m^2Xm^2 matrix with a bunch of As on the diagonals. Do i proceed in the same way when B is not the identity? It looks complicated. (Solving a few easy examples led me to believe that the trace and determinant is the same as in the special case...or maybe i chose bad matrices...) Please HELP!