If A^2=I,B^2=[[3,-2],[2,-1]],AB=[[0,1],[1,0]], find BA.

Kenna Stanton

Kenna Stanton

Answered question

2022-11-10

If A 2 = I , B 2 = [ 3 2 2 1 ] , A B = [ 0 1 1 0 ] , find BA.
What I did was the following: A 2 = I ; A A 1 = I A 2 = A A 1
( A B ) 2 = A B A B [ 0 1 1 0 ] 2 = I A B A B = I B A = A 1 B 1 B A = ( B A ) 1 B A = [ ± 1 0 0 ± 1 ]
which I'm not sure whether it's correct or not and if it's correct, which of these ±s to select from.

Answer & Explanation

Leo Robinson

Leo Robinson

Beginner2022-11-11Added 14 answers

Hint: Use that 0 = t r ( A B ) = t r ( B A ) and 1 = det ( A B ) = det ( B A )

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