##### Exercise6

Suppose that $$A$$ and $$B$$ are $$5\times5$$ matrices such that $$\det A = -2$$ and $$\det B = 5\text{.}$$ Find the following determinants:

1. $$\det(2A)\text{.}$$

2. $$\det(A^3)\text{.}$$

3. $$\det(AB)\text{.}$$

4. $$\det(-A)\text{.}$$

5. $$\det(AB^{-1})\text{.}$$

in-context