Proof of M12=M21 based on stored energy is incorrect

The mutual inductances for a pair of coupled coils are described by a single parameter M instead of two parameters M ₁₂ and M₂₁. Correct proofs of M ₁₂=M₂₁ can be found in books on physics, electromagnetic field theory, and circuit theory written decades ago. In recent years, some authors of textbooks for introductory linear circuit analysis have presented an alternative proof which is seemingly simple, but is actually unsound. The flaw of the proof is shown and a proof based on the calculation of the average power is presented