Which of the following are properties of the rank of a matrix AAA?
rank(A)=rank(AT)\text{rank}(A) = \text{rank}(A^T)rank(A)=rank(AT)
rank(AB)≤min(rank(A),rank(B))\text{rank}(AB) \leq \min(\text{rank}(A), \text{rank}(B))rank(AB)≤min(rank(A),rank(B))
rank(A+B)=rank(A)+rank(B)\text{rank}(A+B) = \text{rank}(A) + \text{rank}(B)rank(A+B)=rank(A)+rank(B)
If AAA is n×nn \times nn×n, rank(A)=n\text{rank}(A) = nrank(A)=n implies AAA is invertible