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Maths-

General

Easy

Question

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

(A⁵ – B⁵)³ = A – B
(A⁵ – B⁵)³ = A³ – B³
A – B is idempotent
A – B is nilpotent

The correct answer is: A – B is nilpotent

Since AB = B and BA = A
$therefore$ A and B both are idempotent
(A – B)² = A² – AB – BA + B² = A – B – A + B = 0
$therefore$ A – B is nilpotent

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