Determinants & Matrices Question 44
Question: If a matrix A is such that $ 3A^{3}+2A^{2}+5A+I=0, $ then what is $ {A^{-1}} $ equal to?
Options:
A) $ -(3A^{2}+2A+5I) $
B) $ 3A^{2}+2A+5I $
C) $ 3A^{2}-2A-5I $
D) $ (3A^{2}+2A-5I) $
Answer:
Correct Answer: A
Solution:
- [a] Let A be a matrix such that $ 3A^{3}+2A^{2}+5A+I=0 $ Post multiply by $ {A^{-1}} $ on both the sides, we get $ 3A^{3}{A^{-1}}+2A^{2}{A^{-1}}+5A{A^{-1}}+I{A^{-1}}=0 $
$ \Rightarrow 3A^{2}+2A+5I+{A^{-1}}=0 $
$ \Rightarrow {A^{-1}}=-(3A^{2}+2A+5I) $
BETA
