Orthogonal projection matrix onto a subspace

Question

Consider vector space $\Bbb R ^n$ and the subspace $\mathbf B \subset \Bbb R ^n $ spanned by the columns of matrix $\mathrm B$. Can it be shown that an orthogonal projection from $\Bbb R ^n$ onto $\mathbf B $ is given by the expression $\mathrm B(\mathrm B^T \mathrm B)^{-1} \mathrm B^{T} \mathrm v = proj_\mathbf B \mathrm v$ ; $\mathrm v \in \Bbb R ^n$ ?