Home
Class 12
MATHS
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

`-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]`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let A and B be two square matrices such that A B=A and B A=B, then A^2=

Let A and B are matrices such that A+B and B A are both defined, then

if A and B are square matrices of same order such that A*=A and B* = B, where A* denotes the conjugate transpose of A, then (AB-BA)* is equal to

If A and B are two matrices such that B=-A^-1 B A then (A+B)^2=

If A and B are two square matrices of the same order such that AB=B and BA=A , then A^(2)+B^(2) is always equal to

If A and B are square matrices of the same order, then

If A and B are square matrices of order 3 , such that |A| =-1 , |B | = 3 , then thee determinant of 3 AB equals :