The matrix \(\mathbf{A}\) is given by
\[\mathbf{A}=\left(\begin{array}{rrr}
5 & -1 & 7 \\
0 & 6 & 0 \\
7 & 7 & 5
\end{array}\right)\]
(a) Find the eigenvalues of \(\mathbf{A}\).
(b) Use the characteristic equation of \(\mathbf{A}\) to find \(\mathbf{A}^{-1}\).