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Let A and B be two n×n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.I. rank(AB) = rank(A)*rank (B)II. det(AB) = det(A)*det(B)III. rank(A+B) ≤ rank(A) + rank(B)IV. det(A+B) ≤ det(A) + det(B) Which of the above statements are TRUE ?(A) I and II only(B) I and IV only(C) II and III only(D) III and IV only |
| Answer» None | |