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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=` `I` b. `2I` c. `O` d. -I

A

`I`

B

`2I`

C

0

D

`-I`

Text Solution

AI Generated Solution

To solve the problem, we need to show that \( A^{-1}B^{r-1}A = A^{-1}B^{-1}A = O \), where \( O \) is the zero matrix. We know that \( B^r = I \) for some positive integer \( r > 1 \). ### Step-by-Step Solution: 1. **Given Information**: We have two non-singular matrices \( A \) and \( B \) of the same order, and it is given that \( B^r = I \) for some integer \( r > 1 \). 2. **Finding \( B^{r-1} \)**: Since \( B^r = I \), we can express \( B^{r-1} \) as: \[ ...
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