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