Properties of Determinants
Properties
Let $A,B$ be a $n\times n$ matrix and $k$ be a constant. The determinant satisfies the following properties:
(a) $\det(kA) = k^{n}\det(A)$
(b) $\det(AB) = \det(A)\det(B)$
(c) $\det(AB)=\det(BA)$
(d) If $A$ is an invertible matrix, then $\det(A^{-1}) = \dfrac{1}{\det(A)}$
(e) $\det(A^{T}) = \det(A)$. Here, $A^{T}$ is the transpose of $A$.