Hi, I have the problem below and I don't know how to solve it... What property do symmetric matrices have that would allow me to solve it without any calculation? Thanks a lot!

So here is the problem:

Find an eigenvector for A (no calculation should be required: note that A is a symmetric matrix).

A =

[1, 1]

[1, -5]

and the eigenvector given is

[2]

[1]