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Suppose A and B are two non singular mat...

Suppose `A` and `B` are two non singular matrices such that `B != I, A^6 = I` and `AB^2 = BA`. Find the least value of `k` for `B^k = 1`

A

`31`

B

`32`

C

`64`

D

`63`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `A^(6)=IimpliesBA^(6)=B`
`implies(BA)A^(5)=B`
`impliesAB^(2)A^(5)=B`
`impliesAB(AB^(2))A^(4)=B`
`impliesA^(2)B^(4)A^(4)=B`
Proceeding like this we get
`A^(6)B^(64)=BimpliesB^(64)=B`
`impliesB^(63)=I`
`impliesk=63`
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