The trace and determinant of a 3x3 matrix satisfy Tr A=2 and det A=2. The sum of two eigenvalues of A is equal to the third eigenvalue. Then the trace and determinant of the matrix $A^2$ is equal to?
I know that the trace is equal to the sum of eigenvalues and determinant is equal to its products.
Let $\lambda_1,\lambda_2, \lambda_3$ be the eigenvalues
Even if i make some substitutions I do not know how to get it for $A^2$.
Please explain how to do this.