kill(all);

A:matrix([c,b],[b,a])/(a*c-b^2);

[[valA,mulA],vecA]:eigenvectors(A)$

B:matrix([a,-b],[-b,c]);

[[valB,mulB],vecB]:eigenvectors(B)$

autovalori uguali e opposti 

fullratsimp([valB[1]*valA[2],valB[2]*valA[1]]);

autovettori uguali

vecB[1]-vecA[2];
vecA[1]-vecB[2];