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If Aa n dB are two non-singular matrices...

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=`

A

`I`

B

`2I`

C

0

D

`-I`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `B^(r) = I rArr B^(r) B^(-1) = IB^(-1)`
`rArr B^(r-1) = B^(-1)`
`therefore A^(-1) B^(r-1) A= A^(-1) B^(-1) A`
` rArr A^(-1) B^(r-1) A- A^(-1) B^(-1) A = 0 `
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