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Idempotent proof 
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#1
Oct1507, 11:35 AM

P: 85

If A and B are idempotent(A=A^2) and AB=BA, prove that AB is idempotent.
this is what i got so far. AB=BA AB=B^(2)A^(2) AB=(BA)^(2) this is where I get stuck. Do A and B have inverses? if so, why? should I be thinking about inverses or is there another way of approaching this problem? 


#2
Oct1507, 12:37 PM

P: 229




#3
Oct1507, 01:27 PM

P: 85

can you just switch the B and A from ABAB to get AABB?



#4
Oct1507, 01:53 PM

P: 633

Idempotent proof
ABAB = A(BA)B = A(AB)B = AABB. Is that OK ?



#5
Oct1507, 02:02 PM

P: 85

i doubt you can switch those matrices b/c youre multiplying the two of them. This has got be wrong. there has to be a different way to get what im trying to get.



#6
Oct1507, 02:31 PM

HW Helper
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#7
Oct1507, 02:31 PM

P: 1,076




#8
Oct1507, 02:32 PM

Sci Advisor
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P: 9,396

As has been pointed out THEY COMMUTE! But that isn't why I post. I want to point out that only in the trivial case can an idempotent be invertible.



#9
Oct1507, 02:42 PM

P: 85

so if i start the proof off with AB=BA then I can use AB=BA later on in the proof I started off with in the firszt place?



#10
Oct1507, 03:02 PM

HW Helper
P: 4,124




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