$A= \begin{bmatrix}-1 & 1 & 1 &1\\ 1 & -1 & 1 &1\\ 1 & 1 & -1 &1\\ 1 & 1 & 1 &-1\\ \end{bmatrix}$ $A$ is a symmetric matrix.Find its eigenvalues?
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix