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?

Let A and B two n × n matrices over real numbers. Let rank(M) and det

1.	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?
A.	I and II only
B.	I and IV only
C.	II and III only
D.	III and IV only
Answer» D. III and IV only