Consider a 2×22 \times 22×2 real matrix AAA with eigenvalues λ=1±2i\lambda = 1 \pm 2iλ=1±2i. What can be said about AAA?
AAA is not diagonalizable over R\mathbb{R}R.
The determinant of AAA is 555.
The trace of AAA is 222.
AAA has real eigenvectors.