Question

# If $$A$$ and $$B$$ are two matrices such that $$AB = B, BA = A$$ then $$[A$$ and $$B$$ are not null matrices].

A
A2=A
B
B2=0
C
AB is idempotent
D
AB is nilpotent

Solution

## The correct option is A $$A^{2} = A$$$$AB=B$$  $$\&$$  $$BA=A$$$$\Rightarrow AB=B$$$$\Rightarrow (BA)B=B$$$$\Rightarrow B(AB)=B$$$$\Rightarrow B.B=B$$$$\Rightarrow B^2=B$$Similarly, $$A^2=A$$Hence, the answer is $$A^2=A.$$Maths

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