# Linear algebra - Orthogonal matrix

## Homework Statement

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.

## Homework Equations

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.