Show that so2 is the group of all 2x2 matrices rtheta

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Reference no: EM13181496

The Orthogonal group On is the set of all nxn matrices with entries in R such that AA^t = 1. The special orthogonal group SOn is the subset of all matrices in On with det(A) = 1.

For each number theta, the matrix Rtheta = (cos, sin; -sin, cos) is in SO2 and represents rotation counterclockwise by an angle of theta. The matrix F = (1,0;01) is in O2 and is the reflection about the x axis.

1. Show that SO2 is the group of all 2x2 matrices Rtheta
2. Show that every matrix in O2 is either Rtheta or Ftheta for some theta.
Hint: What are the cosets

Reference no: EM13181496

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