Bourbaki

Exercise 36, § 9

Lie Groups and Lie Algebras, III, 407

In SL(2,R)\mathbf{SL}(2, \mathbf{R}), the elements which can be expressed in the form (a,b)(a, b), where a,ba, b in SL(2,R)\mathbf{SL}(2, \mathbf{R}), are the elements ≠−I\neq -I.

Solution

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Transcribed from the printed volume. Not translated.