Practice problem
Let AAA and BBB be n×nn \times nn×n matrices. Which of the following facts about the determinant are true?
For t∈Rt \in \mathbb{R}t∈R, det(At)=det(A)t2\det(At) = \det(A) t^2det(At)=det(A)t2
det(AT)=det(A)\det(A^T) = \det(A)det(AT)=det(A)
If AAA is invertible, det(A−1)=det(A)−1\det(A^{-1}) = \det(A)^{-1}det(A−1)=det(A)−1
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)
AAA is invertible if and only if its determinant is zero.
Type a concept, like “slope” or “photosynthesis”.