If A, B are two square matrices such that AB = A and BA = B, then prove that B2
= B

Question

If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B

SHAIK AASIF AHAMED · Answer

Hello student, Given AB=A.........(1),BA=B...........(2) Multiplying 1 and 2 we get AB.BA=AB AB 2 A=AB Premultiplying with A -1 we get B 2 A=B..........(3) also given BA=B....................(4) By comparing 3 and 4 we get B 2 =B Thanks and Regards Shaik Aasif askIITians faculty

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If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B

If A, B are two square matrices such that AB = A and BA = B, then prove that B2
= B

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If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B

If A, B are two square matrices such that AB = A and BA = B, then prove that B2 = B

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If A, B are two square matrices such that AB = A and BA = B, then prove that B2
= B