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A and B are two square matrices such tha...

`A` and `B` are two square matrices such that `A^(2)B=BA` and if `(AB)^(10)=A^(k)B^(10)`, then `k` is

A

`1001`

B

`1023`

C

`1042`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(AB).(AB)=A(BA)B`
`=A^(3)B^(2)`
`(AB)(AB)(AB)=A^(7)B^(3)`
so `(AB)^(n)=A^(z^(n-1))B^(n)`
so `k=2^(10)=1=1023`
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