Answers to Quizlet 5.4

Select the true statements from those below.

1. If A is similar to B, then A² is similar to B².

   True. If A = PBP^-1, then B = P^-1AP, which says B = SBS^-1, if S = P^-1.

2. If A is similar to C, and C is similar to B, then B is similar to A.

   True. If A = PBP^-1 and B = QBQ^-1, then A = P(QBQ^-1)P^-1 = (PQ)B(PQ)^-1.

3. If A and B are similar, then the rank of A may be greater than the rank of B.

   False. In fact, they must have the same rank.

4. If A is similar to B, the Det(A)=Det(B).

   True. They not only have the same determinant, they even have the same characteric polynomial.

Return to Week 10