Find the inverse of the matrix
\[\begin{pmatrix} 5 & -4 \\ 0 & 1 \end{pmatrix}.\]If the inverse does not exist, then enter the zero matrix.
From the formula,
\[\begin{pmatrix} 5 & -4 \\ 0 & 1 \end{pmatrix}^{-1} = \frac{1}{(5)(1) - (-4)(0)} \begin{pmatrix} 1 & 4 \\ 0 & 5 \end{pmatrix} = \boxed{\begin{pmatrix} 1/5 & 4/5 \\ 0 & 1 \end{pmatrix}}.\]