📂Matrix Algebra

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 $A$.