Over the past 20 months, many existential questions have been launched at Manchester United.

What sort of football team were they trying to be? What sort of football did they want to play? And would this sort of football be enough to meet fan expectations? Be it under Erik ten Hag or Ruben Amorim, fans and pundits would wrestle with questions over United’s traditions and how to best take them into modernity. The lustre from the United of old had faded, and the club’s newer form was struggling to establish itself.

One swallow doesn’t make a summer. Two victories for an interim manager do not yet mean United are back. But the manner in which Michael Carrick has earned victory over Manchester City and Arsenal suggests that something has been restored to this squad that was long feared lost.

“United DNA” is a much-discussed and often derided concept, but Carrick and his coaching staff have found a way to make indescribable things easier to grasp.

Question: What are Manchester United?

Answer: A football team that can hurt the biggest clubs in England when the time comes.

Question: How do Manchester United play?

Answer: Like… that.

United took time to find their feet at the Emirates on Sunday. Facing an Arsenal team uniquely equipped to deal with counter-attacks, they struggled to generate the sort of transitional moments that gave Manchester City so much trouble a week before. A run of three consecutive second-place finishes have led Mikel Arteta to build a robust footballing machine that often uses set-piece goals to break down low blocks.

When Lisandro Martinez turned the ball into his own net in the 29th minute, it would have been easy for the match to follow the form book. Arsenal are bigger and stronger than most teams in the Premier League. Their speed and aggression when contesting for second balls means they can starve many good sides of the breathing room and attacking momentum needed to get a result. United, a goal down at the Emirates against the strongest team in the land, were meant to fade into a cold winter evening.

But United did not falter. They were on the back foot but did not blink. It took only a glimpse of goal to get their plans back on track. Martin Zubimendi’s loose pass across Arsenal’s back line saw Bryan Mbeumo spring into action. There are football matches where your opponent’s mistakes can be just as important as your own brilliance; Mbeumo’s decision to chop onto his weaker foot before shooting was an enjoyable mixture of both. David Raya was not ready for a right-footed shot past him. Arsenal had not planned to concede in such a strange manner.

Then it became their turn to blink.

United returned for the second half, ready to throw bodies on the line, lock doors and slam windows shut. If Arsenal were going to win, they would be made to work hard for it. Carrick and his coaching staff have only been in place for a fortnight, but this team has a newfound willingness to execute thankless tasks and channel their creative energies toward the greater good.

Michael Carrick has led Manchester United to two straight victories (Justin Setterfield/Getty Images)

Patrick Dorgu — who caused Amorim to feel anxiety every time he touched the ball — is now playing with a dauntless bravery. His goal in the 50th minute was spectacular, crashing in off the underside of the crossbar and giving his side a much-needed shot of adrenaline. The 21-year-old is not typically a gamebreaker, but he is the sort of hard-working improviser that can be an asset to whatever scheme his coaches put forward. Confidence is not an innate characteristic, but a skill that can be nurtured over time. There is a fire to Dorgu that has been re-ignited.

Carrick’s version of United — for now — has a stronger grasp of who they are supposed to be. United feel more like United in a way that goes beyond tangible actions like tackles made or shots on goal. There is a clarity of vision and purpose to this team that did not get derailed following Mikel Merino’s 84th-minute equaliser. Instead, they dug deeper. They found something to surprise everyone watching. Including those who sat on the United bench.

There are football matches in which one mistake from your opponent can help remind you of your own brilliance. Few expected Matheus Cunha to shoot when standing 30 yards away from Arsenal’s goal. Fewer still expected the ball to nestle so wonderfully in the bottom corner of Raya’s net.

“I can’t take any credit for those two finishes,” said Carrick after the 3-2 win. It can be easy to be hyperbolic after victories over geographical and historic rivals, but the interim head coach has been a stabilising force since his return to the club. His understated media presence allows greater focus on his team. United players look empowered and better prepared for the challenges ahead.

Next Sunday’s match against Fulham will present an obstacle of a different kind. How will this team approach things when they are expected to take the game to an opponent? “It’s a clear focus,” said Carrick of the 15 games that remain for this season. “Everything’s in front of us. Nothing is going to change the past. But it’s a good start. You’ve just got to keep building.”

For now, United sit in a more positive place. They have earned victories through their versatility. Whatever is being built has buy-in from players and fans alike.