Early decision + Early Action

Columbia University says that “While Columbia does not necessarily encourage the filing of both Early Decision (binding) and Early Action (non-binding) applications, we do not prohibit candidates from doing so”.
MIT says that “If you choose to apply to MIT during Early Action, we do not place any limits on where else you may apply, nor do we require you to attend if admitted (though we sure hope you do!). However, if you apply to another school during Early Action that does have a restriction, MIT requires that you respect those rules.”

But, I guess Columbia University doesn’t restrict that. So is it possible to apply Early Action to MIT as well as Early Decision to Columbia University simultaneously?

Yes, some ED schools allow you to apply EA elsewhere.
However, if u are admitted to both, you have to honor your ED commitment and decline EA acceptance.