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in Matrices by (90.2k points)
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If `Aa n dB` are two non-singular matrices of the same order such that `B^r=I ,` for some positive integer `r >1,t h e nA^(-1)B^(r-1)A=A^(-1)B^(-1)A=` `I` b. `2I` c. `O` d. -I
A. `I`
B. `2I`
C. `O`
D. `-I`

1 Answer

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by (95.0k points)
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Best answer
Correct Answer - 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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