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

Emeli Hagan

Emeli Hagan

Answered question

2020-11-10

If A and B are nn matrices, then (AB)2=A22AB+B2

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2020-11-11Added 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
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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