Quadratic form and orthogonality

Question

If the equation $\textbf{x}^T \textbf{x} = \textbf{x}^T M \textbf{x}$ is true for all $\textbf{x}$ and a matrix M in a euclidian vector space, does that imply that M is an orthogonal matrix? And if so, which theorem does that follow from? Unfortunately I could not find anything answering this specific question.