Considering a generic square matrix $A=(a_{i,j})$ we want to compute its inverse $A^{-1}=\left[a^{(-1)}_{i,j}\right]$.
Is there a way to express each $a^{(-1)}_{i,j}$ using a closed form expression?
Considering a generic square matrix $A=(a_{i,j})$ we want to compute its inverse $A^{-1}=\left[a^{(-1)}_{i,j}\right]$.
Is there a way to express each $a^{(-1)}_{i,j}$ using a closed form expression?
The $ij$ entry of $A^{-1}$ is $(-1)^{i+j}$ times the determinant of the matrix $C_{ji}$ obtained by deleting row $j$ and column $i$ from $A$, all divided by the determinant of $A$. I don't know whether you consider that to be a closed form.