
#1
Oct1507, 11:35 AM

P: 87

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: 87

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




#4
Oct1507, 01:53 PM

P: 634

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




#5
Oct1507, 02:02 PM

P: 87

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
P: 4,125





#7
Oct1507, 02:31 PM

P: 1,076





#8
Oct1507, 02:32 PM

Sci Advisor
HW Helper
P: 9,398

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: 87

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: 4,125




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