If a, b, c are right handed system, then so are b, c, a, and c, a, b. In this case, the vectors a, c, b and c, b, a and b, a, c are a left handed system. In order to prove the above statement, I know that the right handed system is positive and the left handed system is negative. So for the second part, b,c,a and c, a, b are right handed because the positions were switched two times, so that makes a right handed system. But, a, c, b and c, b, a and b, a, c are only switched once, so that makes a left handed system. Is this how I prove this statement?