Let T: Rn -> Rn be a linear transformation, and let B be an orthonormal basis for R^n. Prove that [ the length of T(x) ] = [ the length of x ] if and only if [T]B (the B-matrix for T) is an orthogonal matrix.
None I don't think.
The Attempt at a Solution
I've always had a hard time grasping linear transformation problems, so I don't even really know where to start with this one.