For matrix A=(5222)A = \begin{pmatrix} 5 & 2 \\ 2 & 2 \end{pmatrix}A=(5222), which statements are true?
The sum of eigenvalues equals tr(A)=7\text{tr}(A) = 7tr(A)=7
The product of eigenvalues equals det(A)=6\det(A) = 6det(A)=6
The eigenvalues are both positive and distinct
The matrix is orthogonally diagonalizable