The question is that D1 and D2 are any two diagonal 3x3 matrices and
P = AD1Ainv
Q = AD2Ainv
Show that PQ = QP.
Now, I know that D1 and D2 commute, but im not sure how I can show this algebraically. Any ideas?
BTW: A is a 3 x 3 matrix and is the inverse of itself. So, really, P = AD1A and Q = AD2A.
Hi there. Thans for that. But could you explain how you got:
PQ = (AD1A)(AD2A) = A(D1D2)A <-- Since AA = 1
QP = (AD2A)(AD1A) = A(D2D1)A
I'm not sure how you got PQ = A(D1D2)A and QP = A(D2D1)A. What did you do to do that? Rearrange, multiply out?
You can do QP the same way and get
And the rest of the argument goes through as before.
(In case it's an issue, matrix multiplication is associative, that is (AB)C = A(BC), so as long as we don't alter the order of the factors we may insert parenthesis wherever we wish.)