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Let A and B be two non-singular square m...

Let `A` and `B` be two non-singular square matrices such that `B ne I` and `AB^(2)=BA`. If `A^(3)-B^(-1)A^(3)B^(n)`, then value of `n` is

A

`4`

B

`5`

C

`8`

D

`7`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `BA=AB^(2)`
`impliesBA=AB^(2)`
`impliesA=B^(-1)AB^(2)`
`impliesA^(2)=(B^(-1)AB^(2))(B^(-1)AB^(2))`
`=B^(-1)A(BA)B^(2)`
`impliesB^(-1)A AB^(2)B^(2)`
`=B^(-1)A^(2)B^(4)`
`:.A^(3)=B^(-1)A^(3)B^(6)`
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