How to keep column of removed row in matrix

I have matrix A and want to remove the rows of A that have nonzero element. Also want to keep the index of removed columns and rows.

So, when row 3 is removed nonzero element in column 4 and 6 is removed too. I want to keep removed index [3,4,6].

Next we go to remove row 5, so nonzero element in column 6 is removed. want to keep [5,6].

result should be

removed_index={[3,4,6],[5,6]}

A=[0 0 0 0 0 0 0; 0 0 0 0 0 0 0; 0 0 0 1 0 1 0; 0 0 0 0 0 0 0; 0 0 0 0 0 1 0; 0 0 0 0 0 0 0; 0 0 0 0 0 0 0];

[rId, cId] = find(A);
removed_index=[]
for i=1:length(rId)
    
    A(rId(i),:) = 0;
    A(:,rId(i)) = 0;
    
end

Answer 1

[darova]

It was harder that i thought

clc,clear

    % create some data
A = zeros(10);
ix = randi(100,1,10);               % random indices to put 'ones'
A(ix) = 1;
imshow(A,'initialmagnification','fit')
axis on

[rId, cId] = find(A);
n = length( unique(rId) );          % number of cells needed
removed_index = cell(n,1);
[srId,ix] = sort(rId);
scId = cId(ix);
ir = 1; 
i1 = 1;
for i = 1:length(srId)-1
    if srId(i) ~= srId(i+1)
        removed_index{ir} = [srId(i1) scId(i1:i)'];
        ir = ir + 1;
        i1 = i + 1;
    end
end
removed_index{ir} = [srId(i1) scId(i1:end)'];
removed_index{:}

[NA]

I want to get this result,

removed_index={[3,4,6],[5,6]}.

[darova]

I created the code. Look at my previous post