# Orientation Preserving maps

I am a little stumped on the following question. Not sure how to begin.

If $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$ then is $f$ defined by $f(x) = -x$ orientation preserving?

• How are you defining an orientation of $\mathbb{R}^n$? – Zev Chonoles Mar 31 '13 at 5:35
• Not exactly sure. I know what orientable is, just not really what orientation preserving is. – Susan Mar 31 '13 at 5:40
• Does a reflection preserve orientation? – Will Jagy Mar 31 '13 at 5:52

The orientation is preserved if the determinant of the transformation's associated matrix is $+1$. What is the determinant of the matrix associated with $x\mapsto -x$?