Eigenvector/value in linear transformation. I came across this problem



For (a), I wrote $$T(3x,4y) = \lambda (3x, 4y)$$
Since $T$ is a reflection, $\lambda = 1$
That is as far as I got
(b) I simply have no idea. I only know how to find $A$ through brute force. 

Since the point $(4,3)$ is on the line, the reflection will take this point to itself; so this will be an eigenvector corresponding to $\lambda =1$.
Similarly, the point $(3,-4)$ is on the line through the origin perpendicular to the given line; so the reflection will take $(3,-4)$ to its negative $(-3,4)$
and so $(-3,4)$ is an eigenvector corresponding to $\lambda =-1$.
