Chapter 5.7, Problem 406E

A transformation $T:R^2\to R^2,T\left(u,v\right)=\left(x,y\right)$of the form x = au + by. y = cu + dy. where a, b, c, and d are real numbers, is called linear. Show that a linear transformation for which $ad-bc\ne 0$ maps parallelograms to parallelograms.