# Finding the equation of the line over which the linear transformation reflects

I'm trying to find the equation of the line (y=kx) over which the linear transformation, given by the transformation matrix A (it represents reflection over the y-axis):\begin{bmatrix}-1 & 0\\0 & 1\end{bmatrix} reflects. I know how to find k:

-2cosφ = tr(A)

-2cosφ = 0

φ = arccos(0) = 90

k = tg(45) = 1

So now, so I've read, I have to find the eigenvector for the eigenvalue 1:

A-λI = $\begin{bmatrix}-2 & 0\\0 & 0\end{bmatrix}$

How do I procede from here? I see that there is one free variable (y).

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You get that $x = 0$ and $y$ is free so the equation of the line is $x = 0$.