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Any $X\in O^+(n)$ (orthogonal matrices with positive determinant) is the product of an even number of reflection?

I am not able to prove this. Please help.

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    What do you know about $O(n)$ ?2012-07-18
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    $O(n)$ is compact. determinants are $\{+1,-1\}$, collumn vectors are orthonormal.2012-07-18
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    See here http://math.stackexchange.com/q/138020/30357 for an answer without the positivity assumption. To finish an answer to your question, you only need to know how reflections influence the determinant.2012-07-18
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    Hint: what is the determinant of (a matrix representing) a reflection?2012-07-18

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