For an n×nn \times nn×n matrix AAA, which statement is always true?
AAA is invertible ⇔\Leftrightarrow⇔ rank(A)=n\text{rank}(A) = nrank(A)=n
If rank(A)<n\text{rank}(A) < nrank(A)<n, then det(A)≠0\det(A) \neq 0det(A)=0
rank(A)≥n\text{rank}(A) \geq nrank(A)≥n always
ATA^TAT has rank strictly greater than AAA