As long as you do not explain, what the code should achieve, I cannot suggest an improvement.
for i = 1:12
X_t{i} = [A*[i-1;i]];
X_t{i+1} = [A*[i;i-1]];
X_t{i+2} = [A*[i;i]];
end
You can omit the outer square brackets, as MLint most likely suggests already. Then in the first iteration you create the cell elements X{1}, X{2} and X{3}. In the 2nd iteration for i=2, you overwrite X{2} and X{3}, while X{4} is created. Therefore most elements of the cell vector X are overwritten several times and this is not useful. I cannot guess what you want to achieve instead.
Without the brute clearing header, you had a chance to use the debugger by setting a breakpoint. Then steppoing through the code would easily reveal, what's going on inside.
The documentation of quiver (type "doc quiver" in the command window) does not mention any cell arrays. The examples shown there do not use cell arrays also. So why do you want to choose this type to represent your data? Some matrices are more efficient and easier. 
