Given determinant manipulation My homework question says to find the determinant given that $A$ is a $4\times 4$ matrix and its determinant is $-3$. The question is: compute $\det(3A^{-1}).$ I got an answer of $-\frac 1{243}$ and I'm not sure its right. My steps were this $$\det(3A^{-1}) = 3^4 \cdot (-3)\det(A) = -\frac{3}{3^4}.$$ Can anyone confirm that I am doing this properly? My answer seems a little wonky to me. Thanks in advance

No. Your steps are wrong. Here are the right steps: ${\rm det} (3A^{-1})=3^4{\rm det} (A^{-1})=81 ({\rm det} A)^{-1}= 81 (-1/3)=-27$.