Maths-

General

Easy

Question

# If A and B are two matrices such that AB = B and BA = A, then

- (A
^{5} – B^{5})^{3} = A – B
- (A
^{5} – B^{5})^{3} = A^{3} – B^{3}
- A – B is idempotent
- A – B is nilpotent

^{5}– B^{5})^{3}= A – B^{5}– B^{5})^{3}= A^{3}– B^{3}## The correct answer is: A – B is nilpotent

### Since AB = B and BA = A

A and B both are idempotent

(A – B)^{2} = A^{2} – AB – BA + B^{2} = A – B – A + B = 0

A – B is nilpotent

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