Question

If A and B are two matrices such that AB = B and BA = A, then(A6−B5)3=A−B(A5−B5)3=A3−B3A−B is idempotentA−B is nilpotent

Solution

The correct option is D A−B is nilpotentSince 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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