Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesGeneralMedium2 min

MathematicsMediumsingle choice

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

Answer:

Solution:

Since $A B = B$ and $B A = A$ , it follows that A and B are both idempotent.

Therefore, $(A - B)^{2} = A^{2} - A B - B A + B^{2} = A - B - A + B = 0$ .

Thus, $A - B$ is nilpotent.

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:General

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