Computer Sciences > Gate 2020 > Marix Rank
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 ?
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 ?
Correct : c
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