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If A a n d B are two non-singular matric...

If `A a n d B` are two non-singular matrices of the same order such that `B^r=I ,` for some positive integer `r >1,t h e n (A^(-1)B^(r-1)A)-(A^(-1)B^(-1)A)=` a. `I` b. `2I` c. `O` d. -I

A

`I`

B

`2I`

C

`O`

D

`-I`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `B^(r)=I` or `B^(r)B^(-1)=IB^(-1)` or `B^(r-1)=B^(-1)`
`implies A^(-1)B^(r-1) A-A^(-1) B^(-1) A=A^(-1) B^(-1)A-A^(-1) B^(-1)A=O`
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