# Solve this following

Question:

Suppose $A$ is any $3 \times 3$ non-singular matrix and $(A-3 I)(A-5 I)=0$, where $I=I_{3}$ and $O$ $=\mathrm{O}_{3}$. If $\alpha \mathrm{A}+\beta \mathrm{A}^{-1}=4 \mathrm{I}$, then $\alpha+\beta$ is equal to :

1. 13

2. 7

3. 12

4. 8

Correct Option: , 4

Solution: