(Solved): Find the characteristic polynomial and the eigenvalues of the matrix. \[ \left[\begin{array}{ll} 9 ...

Find the characteristic polynomial and the eigenvalues of the matrix. \[ \left[\begin{array}{ll} 9 & 3 \\ 3 & 9 \end{array}\right] \] The characteristic polynomial is (Type an expression using \( \lambda \) as the variable. Type an exact answer, using radicals as needed.) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The real eigenvalue(s) of the matrix is/are (Type an exact answer, using radicals as needed. Use a comma to separate answers as needed. Type each answer only once.) B. The matrix has no real eigenvalues.