What is the importance of the presidential inauguration ceremony towards the peaceful transition of power?

foster some sense of unity,

Explanation:

There were no single ruler that obtain the support of 100% citizens in Democratic countries. Democracy allowed people to pursue their self-interest and elected the leaders that they believe would be the most suitable for their ideals/goals.

So, hostility often occurred between different group of people during the election process.

Inauguration ceremony essentially served as symbolic gesture to remind the people that regardless of our difference, we're still the same citizens of one nation. So, we should respect the decisions of the majority and tried to set aside our difference in order to pursue mutual interest until the next election.

sense of self-interest