If A and B are nn matrices, then (A-B)^2 =A^2-2AB+B^2

Emeli Hagan 2020-11-10 Answered
If A and B are nn matrices, then (AB)2=A22AB+B2
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Expert Answer

lamusesamuset
Answered 2020-11-11 Author has 93 answers
Step 1
Given
(AB)2=A22AB+B2
Step 2
Consider
L.H.S=(AB)2=(AB)(AB)
=(AB)A(AB)B
=AABAABBB
=A2BAABB2
Here L.H.S.=R.H.S is possible only when AB=BA
Consider
A=[1234],B=[2131]
AB=[1234][2131]=[83187]
BA=[2131][1234]=[58610]
ABBA
Hence (AB)2=A22AB+B2
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Jeffrey Jordon
Answered 2022-01-27 Author has 2070 answers

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