試題詳解

4.Let A, B, and C be n x 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 - , then B = C.
(C) If det(AB) 7 0, then A is invertible.
(D) rank(AB)=rank(BA).

(E) None of the above is true.