1. The problem statement, all variables and given/known data 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. 2. Relevant equations None I don't think. 3. 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.