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Let A and B be two non-singular matrices...

Let A and B be two non-singular matrices such
that `A ne I, B^(3) = I and AB = BA^(2)` , where I is the identity
matrix, the least value of k such that ` A^(k)` = I is

A

`4`

B

`5`

C

`10`

D

`7`

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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