One day, as Jesus was teaching the people in the temple and preaching the gospel, the chief priests and the scribes with the elders came up and said to him, “Tell us by what authority you do these things, or who it is that gave you this authority.”
Confrontations are rooted in clear differences, and with this demand, the leaders of the Jews get to the heart of their issue with Jesus. They demand from Him the source of His authority. Jesus was known for teaching so much more differently than any rabbi of His time. His teaching resounded with authority (see Matthew 7:29 for just one example). This bothered the "approved purveyors" of religion because Jesus didn't appear to have their systematically approved credentials, yet vast crowds of people followed Him every place He went. He taught, He healed, He helped... all with authority.
Jesus knew that their demand was contentious, so He asked them to answer a question on authority from Him first. He wanted their opinion on the authority of the baptism of John. And this effectively trapped the jealous, crowd seeking leaders. They'd either be embarrassed to admit they were wrong about John, or they'd risk further alienation from those crowds around Jesus, most of whom had known of John. They refused to answer. And Jesus then refused to enter their debate. He shrewdly got them to surrender first (Luke 20:6-8).
Jesus is the One clearly in charge in this encounter challenging His authority. Why? He is God and is the source of His own authority. He needed no credentials because He spoke the Word of God... quite literally with each conversation. The authority of Jesus is found in His deity. That is why affirming Jesus is God and man, Lord and Savior, are acts of belief and surrender. It is how His authority is recognized and proclaimed.