If AAA and BBB are n×nn \times nn×n matrices, which statement is true?
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)\text{det}(A+B) = \text{det}(A) + \text{det}(B)det(A+B)=det(A)+det(B)
tr(AB)=tr(A)tr(B)\text{tr}(AB) = \text{tr}(A)\text{tr}(B)tr(AB)=tr(A)tr(B)