Question
If A and B are two matrices such that AB = B and BA = A, then
Answer: Option D
:
D
Since AB = B and BA = A
∴ A and B both are idempotent
(A−B)2=A2−AB−BA+B2=A−B−A+B=0
∴ A - B is nilpotent
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:
D
Since AB = B and BA = A
∴ A and B both are idempotent
(A−B)2=A2−AB−BA+B2=A−B−A+B=0
∴ A - B is nilpotent
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