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The SEC hasn’t acknowledged that it’s investigating Tesla, and Ryan White, a spokesman for the agency, declined to comment for this story. A Tesla spokesman also declined to comment.

Musk started 17 days of drama when he tweeted on Aug. 7 that he had “funding secured” to take Tesla private, without sharing evidence that investor money was indeed lined up. Generally, the SEC considers statements by executives to be material information that have to be true, and the comment prompted a subpoena from the regulator.

After Musk has changed course Friday and pledged to keep Tesla public, one of the biggest risks he faces is that the SEC will try to bar him from being an officer or a director of a public company. This level of punishment often stings much more than any fine, which is why most companies aggressively resist it in settlement negotiations with the regulator.

Photo by Kiichiro Sato/AP Photo file

The attention that the go-private-or-not saga generated from Wall Street and the government fuelled speculation that Musk may start to tone down his presence on social media, perhaps at the urging of Tesla’s board, which was put on the defensive by the episode. The company’s chairman and biggest shareholder deactivated his Instagram account last week.

But Musk’s decision to continue to respond to critics on Twitter indicates he won’t change easily, said Charles Elson, a University of Delaware finance professor who specializes in corporate governance.

“If someone has engaged in a course of behaviour for some time, it’s usually difficult to change,” Elson said. “I don’t think a CEO should be on Twitter; I would have hoped that would have been the lesson. Obviously, it’s not.”