試題詳解

4、Let A, B, and C be n×n matrices for some positive integer n. Which of the following statements is/are true?
(A) det( A ) = 0 implies det(R) = 0, where R is the reduced row echelon form of A.
(B) If AB = CA = I_n, then B = C.
(C) If det( AB ) ≠ 0, then A is invertible.
(D) rank( AB )=rank( BA ).
(E) None of the above is true.