‘And it came about, as he was praying apart, the disciples were with him: and he asked them, saying, “Who do the crowds say that I am?” And they answering said, “John the Baptiser. But others say, Elijah, and others, that one of the old prophets is risen again.”
After a time spent in prayer with His disciples, although apart from His disciples (it is significant for His uniqueness that we never read of Him praying together with them), Jesus turned to His disciples who were with Him and asked them what the crowds were saying about Him. This may indicate that He was calling on their knowledge gained on their recent mission, but it may equally simply be a thought provoker leading in to His next question, a question which will hint that He expects better from them than He will receive from the crowds.
Their reply to His first question is in accordance with Luke 9:7-9. It is significant in that it is clear that He had managed to prevent the idea getting around that He was the Messiah. That was the last thing that He wanted volatile Jewish crowds to think, for they had completely the wrong idea about the Messiah, and could quickly have been aroused to fanaticism. John in fact tells us that special ideas had arisen after the feeding of the five thousand when the crowds had begun to think that He was ‘the Prophet who is to come into the world' and had then thought in terms of making Him a king (John 6:14-15). That had been difficult enough. But He had been able to dampen such ideas down. How much worse it would have been if they had actually thought that He was the Messiah. But His behaviour and His preaching had clearly dampened down that idea (hence the puzzlement of John the Baptiser)