If A and B are similar which of the following are true trA

If A and B are similar, which of the following are true? tr(A) = tr (B) rank(A) = nullity(B) The algebraic and geometric multiplicities of the eigenvalues of A and B are the same. A and B have the same eigenvalues. rank(A) = nullity(B^T) A and B have the same eigenvectors.

Solution

Answer :

If A and B are similar then the following are true :

A) tr(A) = tr(B)

C) The algebraic and geometric multiplicities of the eigenvalues of A and B are the same.

D) A and B have the same eigenvalues.

F) A and B have the same eigenvectors.