I have the following question, sorry in advance for my poor mathematical notation, having some serious computer issues!

A a 3x3 matrix:

6 13 -8

2 5 -2

7 17 -9

I was given an eigenvector: v=(1 0 1)^T where its 3x1. I had to find the corresponding eigenvalue which is -2. Then had to show 3 is an eigenvalue and its corresponding eigenvector is (1/2 1/2 1)^T

I am now stuck at the following question:

The matrix A defines a linear transormationT: from real numbers of dimension 3 to the real numbers of dimension 3 by T(x)=Ax. It is known that T fixes a non-zero vector x, T(x)=x. Use this information to determine another eigenvalue of A

Any help would be gratefully received!