Let AAA be a 3×33 \times 33×3 matrix with det(A)=−5\det(A) = -5det(A)=−5. Which of the following is true?
det(AT)=−5\det(A^T) = -5det(AT)=−5
det(2A)=−10\det(2A) = -10det(2A)=−10
det(A−1)=−15\det(A^{-1}) = -\frac{1}{5}det(A−1)=−51
det(−A)=−(−5)=5\det(-A) = -(-5) = 5det(−A)=−(−5)=5