You can just use the formula for determinant
A = rand(3);
d = A(1,1)*(A(2,2)*A(3,3)-A(3,2)*A(2,3)) ...
-A(1,2)*(A(2,1)*A(3,3)-A(3,1)*A(2,3)) ...
+A(1,3)*(A(2,1)*A(3,2)-A(3,1)*A(2,2));
Check if it is correct
>> abs(d-det(A))
ans =
3.4694e-18
A very tiny difference is caused by numerical error.