engineering recuitment GATE IN Test Series 2023-24 Mock Test Engineering Mathematics Linear Algebra Matrix Algebra
Let A and B 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?1
I and II only
2
I and IV only
3
II and III only
4
III and IV only