Prove that a rotation matrix preserves distance

[gottfried]

Homework Statement

Prove that a rotation matrix in R³ preserves distance.

Such that if A is a 3*3 orthogonal rotation matrix then |A.v|=|v|.

I know one can prove this is in R² by using a trig representation of a rotation matrix and then simplifying. Is there an analogue method in R³ or some other more elegant way. A hint/push in the right direction would be nice.

 

[HallsofIvy]

I am puzzled by the question. What, exactly, are you using as a definition of "rotation matrix". If it is the obvious- that it corresponds to a rotation- the fact that it does not change length follows immediately from the definition of "rotation".