Arne Slot's first visit to Manchester United as Liverpool head coach was billed as his most serious examination since succeeding Jurgen Klopp – but he had every answer to pass the test in style.

The Dutchman has made the daunting task of taking over from such an iconic figure as Klopp look easy. His calm, measured approach and clear authority swiftly settling any nerves among supporters that he might have been asked to replace the irreplaceable.

Slot has enjoyed the perfect Premier League start with victories at Ipswich Town and home to Brentford, but the assignment at Old Trafford was always going to carry the most weight and significance in the minds of Liverpool fans and the outside world.

Their 3-0 win was masterly, outclassing United to leave the so-called "Theatre of Dreams" an empire of empty seats long before the final whistle, a result and performance perfectly designed to ensure Slot instantly wins the hearts of his new supporters.

Three wins without conceding a goal does that for any new head coach.

And it looked and sounded exactly like that after the final whistle as Slot's name rang around the small corner of Old Trafford inhabited by the Liverpool fans, with the 45-year-old's under-stated but appreciative response an insight into his character and style.

Slot was concentrating so fiercely during the game that he did not respond to chants from Liverpool's fans and, at the end, there was none of Klopp's fist-pumping histrionics that would have followed such a result. He simply delivered a wave, a clenched fist and then returned applause before marching towards the Stretford End in business-like fashion.

It is very early days but so far Liverpool's transition from Klopp to Slot has been seamless, the Dutchman's task made so much easier by the groundwork of his great predecessor, allied to the quality of the squad bequeathed to him.

Slot is the first Liverpool manager to win his first game against United since Bob Paisley in November 1975 and the second to do so away from home after George Kay in November 1936.

He is also only the third manager to win each of his first three Premier League games without conceding a goal after Jose Mourinho at Chelsea in 2004 and Sven-Goran Eriksson at Manchester City three years later.

The tweaks in style invoked by Slot have been small but important, his intention to adopt a more controlled, pragmatic approach to game management already in evidence.

And this is best exemplified by comparing this Liverpool victory with their games at Old Trafford last season.

The Reds were overwhelmingly dominant before losing the FA Cup quarter-final 4-3 in the final seconds of extra time. The same was true when they needed a late penalty from Mohamed Salah to earn a 2-2 draw in the league.

They were prime examples of the wonderfully entertaining but occasionally chaotic strategy that brought Klopp such great success and so many wild encounters during his time at Anfield.

Here, Liverpool were ruthless and full of menace but always retained control, with not the slightest hint that this hapless Manchester United side would inflict the sort of sucker punches that floored them at Old Trafford last season.

Liverpool pressed United into submission, resulting in Casemiro twice coughing up possession in the build-up to Luis Diaz's two goals in seven minutes just before half-time. The manner in which Alexis Mac Allister did the same to Kobbie Mainoo for Salah's third after 56 minutes merely emphasised the point.

Give this Liverpool team an inch and they will take several miles, as United found to their cost so painfully.

The only cloud on Liverpool's day came after the game when Salah cast serious doubt on his Anfield future with the clear inference that this may well be his final season with a club where he has become an icon.

"Nobody in the club has talked to me about contracts, so OK, I'll play my last season and we'll see at the end of the season," he said. "It's not up to me."

If this is the case, and no-one has any reason to doubt Salah, it is a remarkable state of affairs, with the 32-year-old looking as fit and in form as at any time in his career. He has scored in each of Liverpool's first three games, with his strike against United his 12th in 15 games against them.

If all is as smooth as silk so far for Slot, the same cannot be said for his fellow Dutchman Erik ten Hag, who survived a summer review after winning the FA Cup against Manchester City. An apparent lack of a credible, available replacement helped the decision-making process for Sir Jim Ratcliffe and the new Old Trafford hierarchy.

The reality is Ten Hag is effectively only one bad run, or even one bad result, from coming under severe scrutiny once again. The manner in which Liverpool dismissed United so brutally, coming after their late home win against Fulham and defeat at Brighton, means this will happen with the campaign in its infancy.

Mitigating circumstances must be taken into consideration to put Ten Hag's current plight into context. Midfielder Manuel Ugarte, their new signing from Paris St-Germain, was not available to play, while fellow summer acquisition Leny Yoro is a long-term injury casualty and Mason Mount, Luke Shaw and Rasmus Hojlund are also absent.

This was still, however, a harrowing afternoon for Ten Hag and his players, especially Casemiro when he was a mercy substitution from his manager at half-time, replaced by 20-year-old rookie Toby Collyer.

No such problems for Liverpool as Trent Alexander-Arnold - who had an early goal disallowed for a Salah offside - blew kisses and signalled the 3-0 scoreline to the travelling fans, before walking towards the Stretford End sporting a smile so wide that it looked like it might have to be surgically removed.

The job of succeeding a legendary figure like Klopp was never going to be easy, but Slot is making a very good job of it so far.