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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

Grade:

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Given AB=A.........(1),BA=B...........(2)
Multiplying 1 and 2 we get
AB.BA=AB
AB2A=AB
Premultiplying with A-1we get B2A=B..........(3)
also given BA=B....................(4)
By comparing 3 and 4 we get B2=B
Thanks and Regards
Shaik Aasif
askIITians faculty

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