Question: Show that for a continuous parameter (theta) the set of matrices forms a one-parameter abelian Lie group under matrix multiplication, and that if the matrices

Show that for a continuous parameter $\theta$ the set of matrices

cos e G = sin 0 sin 0 cos 0)

forms a one-parameter abelian Lie group under matrix multiplication, and that if the matrices $G$ operate on a 2D cartesian space $\left(x_{1}, x_{2}\right)$ they leave $x_{1}^{2}+x_{2}^{2}$ invariant.

cos e G = sin 0 sin 0 cos 0)

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