Let $P$ be the matrix of the orthogonal projection of $\mathbb{R}^n$ onto a $m$ dimensional subspace $S\subset \mathbb{R}^n$. Suppose that $\{u_k\}_{k=1}^n$ in an orthonormal basis for $\mathbb{R}^n$ such that $\{u_k\}_{k=1}^m$ is an orthonormal basis for $S$.

Which of these four statements is correct?