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**linear algebra A' is A when two of A lines switched,A Invertible prove (A+A')x=0....**

## Homework Statement

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

## Homework Equations

linear algebra including Determinant

## 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.