# Matrices and Commutativity

1. Sep 27, 2009

### fallen186

1. The problem statement, all variables and given/known data
(Commutativity) Find all 2 x 2 matrices A = [ajk ] that commute with B = [bjk], where bjk = j+k

2. Relevant equations

3. The attempt at a solution
ajk =
1,1
1,1

bjk =
j+k, j+k
j+k, j+k

I am confused about what they are trying to ask me. I understand that commute means that you can reverse it and you will come out with same outcome. I.E. like 3 x 2 = 6 and 2 x 3 = 6. Can someone give me a clue of what I should try to do.

2. Sep 27, 2009

### lanedance

hmmm... not sure i understand the question, does
B
= [bjk] = j + k

=[b11 b12]
_[b21 b22]

=[1+1 1+2]
_[2+1 2+2]?

Then to show commutivity, as you implied, you then need to find all matricies A such that
A.B = B.A = C
where the C is added to clarify the meaning of the sum below, where the dummy indiceis are summed over
cik = aij.bjk = bim.amk

what constraints doe thi put on the values aij