It was girls night out for Madonna and friends as they hit the blue carpet premiere of Ron Howard's new documentary on The Beatles

By Dave Quinn
Updated October 05, 2016 06:19 PM
Credit: Mike Marsland/WireImage

She flew to London on Monday to look after 16-year-old son Rocco during his first week of school. But on Thursday night, it was girls’ night out for Madonna as she hit the premiere of director Ron Howard‘s new documentary on The Beatles.

The film, The Beatles: Eight Days a Week – The Touring Years, chronicles the best-selling band during the years of their initial success, focusing on their history-making world tours and their power as a live act.

With two gal pals by her side, the 58-year-old singer rocked the blue carpet – wearing a button-down black and white varsity dress. Her blonde locks down by her side, Madonna accessorized her look with gold hoop earrings, and array of necklaces and a pair of black Alaïa ankle boots.

“Just perfect,” the Detroit native wrote on Instagram, of the film after its premiere. “An inspiring and sobering reminder of this genius band.”

The movie inspired the “Material Girl” singer to try her hand at her own cover of a classic Beatles tune, singing their 1964 track “A Hard Day’s Night” in an Instagram video with her friends.

Early in the day, a source told PEOPLE exclusively that Madonna’s trip to London was motivated by concerns after ex-husband Guy Ritchie and his wife Jacqui Ainsley had allegedly left Rocco alone before his first day of a new term at school.

“Her kids’ education is the most important thing to Madonna,” the source said. “She takes their schooling very seriously.”

Ritchie’s rep is not commenting.

Her contentious 8-month custody battle with Ritchie ended last week. It began in December when the 47-year-old director refused to return Rocco to his mother for the holidays, despite an order from a New York Supreme Court judge.

The exes’ lawyers hashed it out at a court hearing in March, and the pair appeared to come to a détente in early June, when all parties forwent a scheduled court appearance and court documents showed a motion pending on the case.

RELATED VIDEO: ‘Concerned’ Madonna Flew to London When Ex Guy Ritchie Allegedly Left Son Rocco ‘Alone’ After Custody Agreement: Source

Ritchie’s lawyer told the Associated Press Rocco will remain predominantly in his father’s care in London. A source close to the Snatch filmmaker told PEOPLE back in January that he prefers to employ a more laid-back parenting approach.

“He wants Rocco to have the confidence he lacked growing up and thinks Madonna’s stern parental style is counterproductive,” a Ritchie insider previously said. “The welfare of Rocco is Guy’s priority.”

On Tuesday, Madonna stopped by Rocco’s new school for about an hour and “was very friendly with the teachers and was very relaxed,” a source told PEOPLE of the visit.

Later that night, the mother-son duo enjoyed a quiet dinner at nearby Notting Hill hotspot Farmacy with family friend Benjamin Khalili, a museum curator.

“There was just a really good vibe. Everyone was smiling and laughing the whole evening. It was a very nice evening for them all,” an onlooker told PEOPLE at the time, adding Rocco “was just loving life and spending quality time with his mum.”