【行列式編】逆行列の求め方を画像付きで解説！ | 大学1年生もバッチリ分かる線形代数入門

A−1=1∣A∣t[Aij]=1∣A∣(A11A21⋯An1A12A22⋯An2⋮⋮⋱⋮A1nA2n⋯Ann)\begin{aligned} A^{-1} &=\frac{1}{|A|}{}^t[A_{ij}] \\ &=\frac{1}{|A|} \left( \begin{array}{cccc} A_{11} & A_{21} & \cdots & A_{n1} \\ A_{12} & A_{22} & \cdots & A_{n2} \\ \vdots & \vdots & \ddots & \vdots \\ A_{1n} & A_{2n} & \cdots & A_{nn} \end{array} \right) \end{aligned}A−1​=∣A∣1​t[Aij​]=∣A∣1​​A11​A12​⋮A1n​​A21​A22​⋮A2n​​⋯⋯⋱⋯​An1​An2​⋮Ann​