Gate2020 cs Q55

0. 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?

Answer
Comment
Array

Option : D
Explanation :
d(AB) = d(A) × d(B)
d(A + B) ≥ d(A) + d(B)
r(A + B) ≤ r(A) + r(B)
r(AB) ≠ r(A) r(B)

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