In short, we can writeµxy¶A7→µx0y0¶B7→µx0y0¶.Since the two lines are perpendicular, we see from the picture that these 3 points arevertices of a right-angled triangle and that the origin is at the midpoint of its hypotenuse.Thusµx0y0¶=−µxy¶=µ−x−y¶.Since the matrix productBAcorresponds to the composition ofAfollowed byB,weconcludeµxy¶=µ−x−y¶,sois the reﬂection about the origin, i.e. the rotation by 180◦. Now we can write thematrix:=µcos(180◦)−sin(180◦)sin(180◦)cos(180◦)¶=µ−100−1¶.This can also be seen fromµxy¶=µ−x−
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This note was uploaded on 04/12/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.