逆矩阵

${\displaystyle \mathbf {A} ={\begin{bmatrix}1&2\\3&4\end{bmatrix}}}$

性质

1. ${\displaystyle \left(A^{-1}\right)^{-1}=A}$
2. ${\displaystyle (\lambda A)^{-1}={\frac {1}{\lambda }}\times A^{-1}}$
3. ${\displaystyle (AB)^{-1}=B^{-1}A^{-1}}$
4. ${\displaystyle \left(A^{\mathrm {T} }\right)^{-1}=\left(A^{-1}\right)^{\mathrm {T} }}$ ${\displaystyle A^{\mathrm {T} }}$ 为A的转置
5. ${\displaystyle \det(A^{-1})={\frac {1}{\det(A)}}}$ （det为行列式