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Question

If A and B are two matrices such that AB = B and BA = A, then
  1. (A6B5)3=AB
  2. (A5B5)3=A3B3
  3. AB is idempotent
  4. AB is nilpotent


Solution

The correct option is D AB is nilpotent
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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