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. Which of the following statements is/are true?
1
rank(AB) = rank(A) rank(B)
2
det(AB) = det(A) det(B)
3
rank(A + B) ≤ rank(A) + rank(B)
4
det(A + B) ≤ det(A) + det(B)