Find the matrix $\mathbf{P}$ such that for any vector $\mathbf{v},$ $\mathbf{P} \mathbf{v}$ is the projection of $\mathbf{v}$ onto the $yz$-plane.
The projection $\mathbf{P}$ takes $\begin{pmatrix} x \\ y \\ z \end{pmatrix}$ to $\begin{pmatrix} 0 \\ y \\ z \end{pmatrix}.$

[asy]
import three;

size(180);
currentprojection = perspective(6,3,2);

triple I = (1,0,0), J = (0,1,0), K = (0,0,1), O = (0,0,0);
triple V = (2.2,2.5,2.5), W = (0,2.5,2.5);

draw(V--W,dashed);
draw(O--V, red, Arrow3(6));
draw(O--W,blue, Arrow3(6));
draw(O--3*I, Arrow3(6));
draw(O--3*J, Arrow3(6));
draw(O--3*K, Arrow3(6));

label("$x$", 3.2*I);
label("$y$", 3.2*J);
label("$z$", 3.2*K);
label("$\mathbf{v}$", V, NW);
label("$\mathbf{w}$", W, NE);
[/asy]

Thus,
\[\mathbf{P} \mathbf{i} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}, \quad \mathbf{P} \mathbf{j} = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \quad \mathbf{P} \mathbf{k} = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix},\]so
\[\mathbf{P} = \boxed{\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}}.\]