The question:

Show that (1, -2) and (2, -3) are eigenvectors of A and find the corresponding eigenvalues, for

My attempt:

I just multipled the eigenvectors by the matrix, then found the eigenvalues by inspecting which multiple to use to get this new vector. This gets the correct solution, but I'm wondering if this is sufficient since it says to "show that" they're eigenvectors.

Thanks.