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=`
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. 0
D. `-I`
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Correct Answer - 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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