If AAA is an invertible n×nn \times nn×n matrix, which of the following is true?
det(A−1)=1det(A)\det(A^{-1}) = \frac{1}{\det(A)}det(A−1)=det(A)1
(AT)−1=(A−1)T(A^T)^{-1} = (A^{-1})^T(AT)−1=(A−1)T
det(A)≠0\det(A) \neq 0det(A)=0
An=0A^n = 0An=0 for some nnn