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if `A and B` are squares matrices such that `A^(2006)=O and A B=A+B , then ,"det"(B)` equals a.`0` b. `1` c. `-1` d. none of these

A

`-1`

B

`0`

C

`1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`because AB = A+B`
`rArr B= AB - A = (B-I)`
`rArr det (B) = det (A) cdot det (B-I) = 0" "[because A^(2006 )=0rArr det A^(2006) = 0 ] [therefore det A=0]`
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