def _adjugate(M, method="berkowitz"):
    """Returns the adjugate, or classical adjoint, of
    a matrix.  That is, the transpose of the matrix of cofactors.

    https://en.wikipedia.org/wiki/Adjugate

    Parameters
    ==========

    method : string, optional
        Method to use to find the cofactors, can be "bareiss", "berkowitz" or
        "lu".

    Examples
    ========

    >>> from sympy import Matrix
    >>> M = Matrix([[1, 2], [3, 4]])
    >>> M.adjugate()
    Matrix([
    [ 4, -2],
    [-3,  1]])

    See Also
    ========

    cofactor_matrix
    sympy.matrices.common.MatrixCommon.transpose
    """

    return M.cofactor_matrix(method=method).transpose()