Why during interview when hiring your team it is useful to involve in interview someone from your team members?

Team members will gauge the prospective team member from their point of view and they are the best judge , secondly later on they will not approach with complaints and excuses, thirdly a sense of togetherness will be there all the time since they were involved right from the beginning. 

To choice the right people to achieve the team goal.

Two heads are better than ONE, in hiring, final decision shud be made via a panel or so.

It is not necessary or mandatory to involve team members, this should be done carefully. Involving a team member during the interview process sends across a positive message to all other team members and if the candidate does end up getting hired - he/she is well received by the team.

However it is important to be noted that you should be driving the interview and avoid discussions on sensitive subject like compensation, family etc during this interview, stick to job requirements. You do not want your team to start gossiping (its human nature, you cannot stop it) about the candidate.

That there will be three people person from employment - Administration Manager - another employee of the same department in order to be consensus or decision one

The team knows what it lacks, therefore they would make a decision if candidate qualifies for the position and is able to contribute or has something to bring to the table..