cofactor method

Given a square matrix \( A \) of order \( n \), the inverse of \( A \), denoted by \( A^{-1} \), is defined (if it exists) as the matrix such that its product with \( A \) results in the identity matrix. In symbols:

\[
A \cdot A^{-1} = A^{-1} \cdot A = I
\]