Let $3\times 3$ matrices $A$ and $B$ have determinants $-1$ and $2$, respectively.
A) Find determinant of $(2A)B^{-1}$
B) Find determinant of $B^2A^{-1}$
C) Find a scalar $c \in \Bbb R$ such that the $\det[(cA)B]=1$
D) Find the determinant of $A^{2016}$
I understand how to find determinants. Could I just make up my own matrices that have the determinants of $-1$ and $2$ and apply that to each question?
Yes, you could do that and you would get the right answers. However, I suggest not doing that because that's kind of unnecessary. All you need are the following determinant rules: $$\det(AB)=\det(A)\cdot\det(B)$$ $$\det(A^p)=\det(A)^p$$ $$\det(A^{-1})=\frac{1}{\det(A)}$$ $$\det(cA)=c^n\det(A)$$ (Note that in the last equation, $n=3$ since we're working with 3x3 matrices.)