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

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

[From: ] [author: ] [Date: 11-04-28] [Hit: ]

the answer is A+B

given AB=A and BA=A
A^2+B^2=AA+BB
=BABA+ABAB
=BBA+AAB(since ab=b and ba=a)
=BA+AB(since ba=a and ab=b)
=A+B(since ba=a and ab=b)

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