1.
Let A=(1225)A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix}. Let α,βR\alpha, \beta \in \mathbb{R} be such that αA2+βA=2I\alpha A^2 + \beta A = 2 I. Then α+β\alpha + \beta is equal to: