A complex 2×22 \times 22×2 matrix has eigenvalues λ1=2+3i\lambda_1 = 2 + 3iλ1=2+3i and λ2=2−3i\lambda_2 = 2 - 3iλ2=2−3i. Which properties must be true?
The matrix is orthogonally diagonalizable over R\mathbb{R}R
The matrix is symmetric
The matrix has trace tr(A)=4\text{tr}(A) = 4tr(A)=4 and determinant det(A)=13\det(A) = 13det(A)=13
The matrix must be real