Do a row reduction: look at what happens when you subtract, say, times the first row from the second. Try it with a 2 by 2 matrix first.
Many thanks for your reply.
It holds when M is a 2 by 2 matrix.
I tried using row reduction, most items become same but there still exist some items uncertain.
In fact, I am perplexed by this problem for such a long time and I have tried using induction but failed.