In Chapter 3, we said that any 3-by-3 orthogonal matrix with determinant =-1 can be written in the form (7.19). Use this and Problem 1 to show that in 3 dimensions, an inversion (that is a reflection through the origin so that all three axes are reversed) is equivalent to a reflection through a plane combined with a rotation about the line perpendicular to the plane [say a reflection through the (x, y) plane-that is, a reversal of the z axis-and a rotation of the (x, y) plane about the z axis]. Hint: Consider the matrix B in Chapter 3, (7.19).
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