Which of the following is true for any two n×nn \times nn×n matrices AAA and BBB?
rank(A+B)=rank(A)+rank(B)\text{rank}(A+B) = \text{rank}(A) + \text{rank}(B)rank(A+B)=rank(A)+rank(B)
rank(A+B)≤rank(A)+rank(B)\text{rank}(A+B) \leq \text{rank}(A) + \text{rank}(B)rank(A+B)≤rank(A)+rank(B)
det(A+B)=det(A)+det(B)\det(A+B) = \det(A) + \det(B)det(A+B)=det(A)+det(B)
det(AB)=det(A)+det(B)\det(AB) = \det(A) + \det(B)det(AB)=det(A)+det(B)