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If A and B are two matrices such that AB =B and BA = A, then $A^{2} + B^{2}$ is equal to

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2AB

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detailed solution

Correct option is C

We have A2+B2=(BA)2+(AB)2=(BA)(BA)+(AB)(AB)=B(AB)A+A(BA)B=B(BA)+A(AB)=BA+AB=A+B.

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If A and B are two matrices such that AB =B and BA = A, then A2+B2 is equal to

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If A and B are two matrices such that AB =B and BA = A, then $A^{2} + B^{2}$ is equal to