Given a matrix $A = \begin{pmatrix} 40 & -29 & -11\\ \ -18 & 30\ & -12 \\\ \ 26 &24 & -50 \end{pmatrix}$ has a certain complex number $l\neq0$ as an eigenvalue. Which of the following must also be an eigenvalue of $A$: $l+20, l-20, 20-l, -20-l?$
It seems that complex eigenvalues occur in conjugate pairs. It is clear that the determinant of the matrix is zero, then $0$ seems to be one of the eigenvalues.
Please suggest.