Lets try it now with a character matrix:
A = ['0110';'1010'];
writematrix(A,'test.txt')
type test.txt
No double quotes added.
Lets try a string array:
A = ["0110";"1010"];
writematrix(A,'test.txt')
type test.txt
No double quotes added.
What does reproduce your screenshot is when the data itself contains trailing commas (i.e. field delimiters):
A = ['0110,';'1010,'];
writematrix(A,'test.txt')
type test.txt
Solution: remove the trailing commas from the data OR specify the QuoteStrings option:
A = ['0110,';'1010,'];
writematrix(A,'test.txt', "QuoteStrings","none")
type test.txt

