Quote by fuzzyorama
Ahh.. so I don't actually need to multiply the eigenvector with the eigenvalue to see if they are equal?

Yes you still need to. Remember, the idea here is finding a vector that when acted upon by your matrix A, you return the vector multiplied by the eigenvalue. No matter what constant you multiply your eigenvector by, that is x > cx where c is a constant, when you multiply from the left with A you still must return that eigenvalue multiplied by cx.