suppose T is a linear transformation on R^2 (i.e T(z,y)=(ax+by, cz+dy) where a,b,c,d are real numbers and, interpreting T as a matrix, (T) # 0. Let P be the parallelogram which is the image of the square D=[0,1] x [0,1] {i.e T(D)=P}. The the area of P is given by