How to show an antisymmetric matrix satisfies Rx=zy and Ry=-zx

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Homework Statement


Hi, If I have an antisymmetric matrix R, how might I show that there are real 3D vectors x and y and some real number z such that
Rx=zy and Ry=-zx?
Thanks!

Homework Equations


Rx=zy and Ry=-zx

The Attempt at a Solution


I know that it is true intuitively because it is like a rotation matrix... but am not quite sure how to show it...
 
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