A friend of mine will send me an invitation letter. I do not require Schengen tourist visa, but I could have an invitation letter. So, when he has the approved letter of invitation, should I show it in original in airport or it's okay if I travel with a scanned one?
Invitation letters are not generally required. If immigration officers doubt your stated purpose, they will likely want to phone your friend to confirm it. If the officers believe you, they won't ask for evidence to support your claim.
Invitation letters are easily forged, so they don't have a great deal of evidentiary value. A copy of an invitation letter may have slightly less value than an original, but "less than not a great deal" is still "not a great deal."