Let A and B any two n xx n matrices such...

Let A and B any two `n xx n` matrices such that the following conditions hold : `AB= BA` and there exist positive integers `k` and `l` such that `A^(k)=I` (the identity matrix) and `B^(l)=0` (the zero matrix). Then-

A

`A + B = I`

B

det (AB) =0

C

det `(A + B) ne 0`

D

`(A + B)^(m)= 0` for some integer m

Verified by Experts

The correct Answer is:

B

`A^(k)=I, B^(l)=0 ("det (B) = 0")`
`rArr" det "(AB)=0`

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