Determinants Matrices Question 43
Question: If A and B are two nonsingular matrices of the same order such that B-=I, for some positive integer r>1, then $ {A^{-1}}{B^{r-1}}A-{A^{-1}}{B^{-1}}A $ =
Options:
A) I (Incomplete statement, no correction applied as no full context provided)
B) 2I
C) O₂
D) -I
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ B^{r}=I $ or $ B^{r}B^{-1} $
$ =I{B^{-1}} $ or $ {B^{r-1}}={B^{-1}} $
$ \Rightarrow {A^{-1}}{B^{r-1}}A-{A^{-1}}{B^{-1}}A $
$ ={A^{-1}}{B^{-1}}A-{A^{-1}}{B^{-1}}A=O $
BETA
