Adjoint Matrix, also known as adjugate matrix, is a matrix that if formed by the transpose of the cofactor matrix for any given square matrix.
Adjoint of matrix is not only used to find the inverse of a matrix. Even if the inverse of matrix don't exist, adjoint of a matrix is well-defined and meaningful.
Even if inverse don't exists, adjoint of matrix exists and is well-defined
Calculating the adjoint of matrix is a simple process.
Form a new matrix with the same dimenions as the original matrix. And for all elements replace the elements with the cofactor of the original matrix.
Co-factor of the matrix