Algebra
If A, B are two square matrices such that AB = A and BA = B, then prove that B2
= B
1 Answer
SHAIK AASIF AHAMED
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
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