I have a matrix $$ \begin{pmatrix} 0 & i & 0 \\ -i & 0 & 1 \\ 0 & 1 & 2 \\ \end{pmatrix} $$
Since this matrix is Hermitian, we know that it should be unitarily diagonalizable. But when I try to solve the characteristic polynomial, it turns to be $-t^3+2t^2+2t-2$, I have difficulty guessing one of the roots. Can anyone help? Or did I make some mistake? Thanks.