I am currently learning matrix transformations and ran in to an exercise that I can't understand. We start with e1 = (1,0) e2 = (0,1) So the first transformation is a shear one where e2 becomes -2e1 + e2, after that transformation I need to reflect the matrix with regard to line y = -x. So when I draw e1 (1,0) and e2 (-2,1) and reflect them I get that e1 becomes (0,-1) and e2 becomes (2,-1), but the answer differs from the one I got cause e2 should become (-2,-1). According to the formula when reflecting (multiply top left and bottom right by -1 and switch rows). Where do I go wrong, can't you draw and reflect based on your drawing? Thanks.