Two matrices A and B are called similar if there exists another matrix S such that S−1AS = B. Consider the statements:
(I) If A and B are similar then they have identical rank.
(I) If A and B are similar then they have identical trace.
(III)
Which of the following is TRUE.
(A) Only I and III
(B) Only II
(C) Both I and II but not III
(D) All of I, II and III
