Matrices

Question
If A and B are two matrices such that AB = B and BA = A, then
Options:
A. (A6−B5)3=A−B
B. (A5−B5)3=A3−B3
C. A−B is idempotent
D. A−B is nilpotent

 Next Question
Answer: Option D
: D

Since AB = B and BA = A
A and B both are idempotent
(AB)2=A2ABBA+B2=ABA+B=0
A - B is nilpotent

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