Let AAA be a 3×33 \times 33×3 invertible matrix with det(A)=−3\det(A) = -3det(A)=−3. What is det(4A−1)\det(4A^{-1})det(4A−1)?
4−3=−43\frac{4}{-3} = -\frac{4}{3}−34=−34
43−3=−643\frac{4^3}{-3} = -\frac{64}{3}−343=−364
43×(−3)=−1924^3 \times (-3) = -19243×(−3)=−192
4×1−3=−434 \times \frac{1}{-3} = -\frac{4}{3}4×−31=−34