Properties of Determinants

$$\begin{array}{r}\det (kA)=k^n\det (A)\\ \\ \det (AB)=(\det A)(\det B)\\ \\ \det (A^k)=(\det A{)}^k\\ \\ \det (A^T)=\det (A)\\ \\ \det (A^{-1})=\frac{1}{\det (A)}\\ \\ \det (A+B)\ne \det (A)+\det (B)\end{array}$$