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if A and B are squares matrices such tha...

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

0

B

1

C

`-1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`AB=A+B`
or `B=AB-A=A(B-I)`
or det `(B)=` det (A) det `(B-I)=0`
or det `(B)=0`
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