Determinants Matrices Question 93
Question: If $ A^{3}=0 $ , then I=A+ $ A^{2} $ equals
Options:
A) $ I-A $
B) $ {{(I+A^{1})}^{-1}} $
C) $ {{(I-A)}^{-1}} $
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] Given $ A^{3}=0 $ Now, $ (I-A)(I+A+A^{2}) $
$ =I^{2}+IA+IA^{2}-AI-A^{2}-A^{3} $
$ =I-A^{3}=I $
$ \Rightarrow {{(I-A)}^{-1}}=I+A+A^{2} $
BETA
