Determinants Matrices Question 109
Question: If A is a square matrix such that $ (A-2I)(A+I)=O $ then $ {A^{-1}}= $
Options:
A) $ \frac{A-I}{2} $
B) $ \frac{A+I}{2} $
C) $ 2(A-I) $
D) $ 2A+I $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ (A-2I)(A+I)=0\Rightarrow AA-A-2I=0 $
$ \Rightarrow A( \frac{A-I}{2} )=I\therefore \frac{A-I}{2}={A^{-1}} $
BETA
