MATLAB: Sum each page of a 3D matrix and append sums as rows of new 2D matrix

for loops

I cannot for the life of me figure out why this for loop is overwriting the first row of my output variable (D). I have spent a few hours now reading through Matlab forums/documentation, and it appears that I've written this correctly but it's still overwriting.
I have a 2D matrix (A), a second 2D matrix (B), and I've concatenated these to make a 3D matrix (C) where Page 1 = A and Page 2 = B. I want to sum each page of C and name D such that each row of D is the sum of each column of each page in C. So, the final output for D should be [15 15 15; 25 25 25]. I believe the output is [0 0 0 ; 25 25 25] because Matlab is overwriting the first iteration of the for loop and pasting only the results of the second (and final) iteration.
Example code:
A = [5 5 5; 10 10 10]
B = [15 15 15; 10 10 10]
C = cat(3,A,B)
D = zeros(2,3)
for i = 2
    D(i,:) = sum(C(:,:,i),1)
end
Where am I going wrong?
Thank you in advance.

Best Answer

D=permute(sum(C,1),[3,2,1])
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