linear algebra A' is A when two of A lines switched,A Invertible prove (A+A')x=0.... 1. The problem statement, all variables and given/known data A is a n*n matrix A' is the matrix A when two two lines i,j are switched. (switch two random lines is A and you get A') If A Invertible Prove that the system (A+A')x=0 has infinite solutions 2. Relevant equations linear algebra including Determinant 3. The attempt at a solution Well I know that A+A' has two identical lines so when subtracting them I get a line of 0 and then Because I know there is a line of 0 I know that there are infinite solutions... But I did not used the fact that A is Invertible... How do I solve it while using this fact? , I try to use Determinant but I do not mange to. Thank you.