A linear operator L: V V, where V is an n-dimensional Euclidean space, is called orthogonal

Question:

A linear operator L: V → V, where V is an n-dimensional Euclidean space, is called orthogonal if (L(x), L(y)) = (x, y). Let S be an orthonormal basis for V, and let the matrix A represent the orthogonal linear operator L with respect to S. Prove that A is an orthogonal matrix?