Let A = ({1 2} {-2 -5}). Let α,β ∈ R be such that αA^2 + βA = 2I . Then α + β is equal to - ​

Question

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

(A) -10

(B) -6

(C) 6

(D) 10

Answer 1

Correct option is (D) 10

Characteristic equation of matric A