2. Let T : R² →> R² be defined by T(x) = Ax, where A is the following matrix: (1/2-1/2) (a) Sketch the image of the unit square (vertices at (0, 0), (1, 0), (1, 1), and (0, 1)) under the transformation T. (b) Based on your sketch, determine whether T is one to one, and whether T is onto. Your answer should include a brief discussion of your reasoning, based on the geometry of the transformation. (c) Prove your conjecture about whether T is one-to-one using the definition of a one-to-one map. (d) Prove your conjecture about whether T is onto using the definition of an onto map.