What Matrices A Commute with a Given 2x2 Matrix B?

[fallen186]

Homework Statement

(Commutativity) Find all 2 x 2 matrices A = [a_jk ] that commute with B = [b_jk], where b_jk = j+k

Homework Equations

The Attempt at a Solution

a_jk =
1,1
1,1

b_jk =
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.

 

[lanedance]

hmmm... not sure i understand the question, does
B
= [b_jk] = 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
c_ik = a_ij.b_jk = b_im.a_mk

what constraints doe thi put on the values a_ij