Question 147
Let $A \in M_{2}(\mathbb{C})$ with $A^{2}-3 A+5 I_{2}=O_{2}$.
a) Find the inverse of the matrix $A$.
b) Compute $\operatorname{det}\left(A^{2}-I_{2}\right)+\operatorname{det}\left(A^{2}+A\right)-\operatorname{det}\left(A^{2}+2 I_{2}\right)$.
a) Find the inverse of the matrix $A$.
b) Compute $\operatorname{det}\left(A^{2}-I_{2}\right)+\operatorname{det}\left(A^{2}+A\right)-\operatorname{det}\left(A^{2}+2 I_{2}\right)$.