Let $\mathbf{M} = \begin{pmatrix} p & q \\ r & s \end{pmatrix}.$  Then
\[\mathbf{M} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} p & q \\ r & s \end{pmatrix} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} pa + qc & pb + qd \\ ra + sc & rb + sd \end{pmatrix}.\]We want this to be equal to $\begin{pmatrix} c & d \\ a & b \end{pmatrix}.$  We can achieve this by taking $p = 0,$ $q = 1,$ $r = 1,$ and $s = 0,$ so $\mathbf{M} = \boxed{\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}}.$
Find the matrix $\mathbf{M}$ that swaps the rows of a matrix.  In other words,
\[\mathbf{M} \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} c & d \\ a & b \end{pmatrix}.\]If no such matrix $\mathbf{M}$ exists, then enter the zero matrix.
{'answer': '\\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix}', 'subject': 'Precalculus', 'level': 3, 'unique_id': 'test/precalculus/945.json'}