As early as 2004, an acquaintance leaned over to me during an M.I.A. show and sneered: "She's totally faux, you know." Accusations of inauthenticity rumbled away in the background even as she progressed from hipster cult audiences to international recognition - and they seemed to come to a head during an infamous New York Times interview with Lynn Hirschberg in 2010, as M.I.A. was gearing up to release her third album, /\/\/\Y/\. Hirschberg unsubtly depicted the rapper and producer, then affianced to Brentwood billionaire Benjamin Bronfman, as a woman of privilege whose much-touted politics were shallow and confused.

Inevitably, the truth seems more complicated. On the one hand, the former art student's politics have often amounted to little more than insubstantive sloganeering on record; she's conflated disparate global conflicts unhelpfully; Sri Lankan activists have accused her of misrepresenting the situation in her home country; and, of late, her support of (and collaboration with) egomaniac and accused rapist Julian Assange has left a sour taste in the mouth. On the other: what is M.I.A.'s "authenticity", for whatever that means, supposed to look like? Why have white journalists taken it upon themselves to warn the public, "Don't let M.I.A.'s brown skin throw you off," as Simon Reynolds did so memorably in 2005? Her habit of being a musical magpie, hovering over worldwide street genres from funk carioca to kuduro and snatching up the shiniest stuff, has left her open to charges of appropriation - but searching for a scene to call home, and invariably moving on, is also true to the lived experience of a second-generation immigrant.

But appropriately enough on an album whose title is a play on her own name, M.I.A. sounds more herself on Matangi than she ever has before. The genre tourism quotient is almost nil, the specific references to global scenes largely abandoned. The most overt interpolation is, unexpectedly and delightfully, of Shampoo's 1994 punk-pop hit 'Trouble' - a tongue-in-cheek reminder of her own 90s indie kid roots. Instead, Matangi is a collage of cacophonous percussion, chants, chirps, squawks, stutters, digital distortion, the occasional beautiful breathing space and, front and centre, M.I.A.'s voice ringing out scornfully. The title track sets out the album's stall uncompromisingly: ideas pop up from nowhere and retreat for good within the space of a few bars, from trap snares to bird noises to the degraded Arabic melody the song winds down with. Matangi sounds like a mess on first, second and third listen - and it doesn't help that the album's worst missteps, the lumbering Britpop-worthy ballad 'Come Walk With Me' and the squeaky irritant 'aTENTion', weigh down its first half. But when it coheres, it's a thrill.

Her political sloganeering may have been shallow - but the flipside of that has always been that M.I.A. can sell a slogan like few others. Nonsense phonetics and exhortative wordplay have always been her forte, and Matangi finds her on scorching, knowing form. She drops the beat out and cuts up her words to accentuate her best one-liners: "Lara Croft is soft when it comes to my stuff," "Looking through your Instagram, looking for a pentagram," "My nan was a stan for imported liquor brands," "I'm a party fucking animal - if you ain't, scram!" And for a woman whose charisma has always surpassed her actual technical skill, whether rapping or singing, her ability to employ a variety of vocal modes is key to her success: a childish sing-song to taunt white privilege on 'Boom Skit', lullabic gentleness with an edge of anger on 'Lights', as though she's passing reasons to fight down to her son; the sheer clattering, relentless energy with which she charges at the album's bangers and highlights, 'Warriors', 'YALA' and 'Bring The Noize'. She even manages to deliver the first great ballad of her career: 'Exodus', reprised as 'Sexodus', displays the grandeur of first the protest march and then the bedroom, the gothic cloak of the production ruptured by attention-seizing beats in a manner reminiscent of Dawn Richard.

Any polemic needs a target - and Matangi's are, loosely, banks and bros. Regarding the latter, M.I.A. cuts them dead with sly wit. She's described the album as a document of living through "the time of the bros" as embodied by, variously, her custody battle and the YOLO cod philosophy. Matangi's two separate incidences of Drake shade are deeply satisfying, of course: 'YALA', which pretends to be a stripper anthem but winds up sounding like a stripper rebellion, reads YOLO to filth and renders it redundant. Even better is the way it's spurred M.I.A. to come out fighting. At 38, she sounds as hungry and angry as any up-and-comer. If her last album represented a bubble bursting - artistically flat and underwhelming, a critical and commercial failure accompanied by a hitherto enthralled music press turning on her and followed by personal upheavals - then Matangi is the sound of M.I.A. lashing back, throwing elbows, reasserting herself. There's a lot at stake for her here, and it shows.

For example: there are few sounds as satisfying as M.I.A. biting gloriously into the lines, "Banking offshore - take a trip to Singapore - I need to earn like I'm Julianne Moore." It's a reminder, too, that she's always been explicit about aiming for wealth, in that desperate but deeply felt way that will resonate with anyone who's spent a long time around, but not of, wealth. Truffle fries cannot be used against her. When she elides this with the sundry jabs she takes at the financial system throughout Matangi, M.I.A. comes up with her most electrifying call to arms yet on 'Only 1 U': "There's trillions of cash, and there's billions of us, and there's millions of things that can happen with this stuff; and there's thousands that will crash, and there's hundreds that will smash; there's only one you and I'mma drink to that." Trickle-down revolution to replace trickle-down economics.

"I sleep on my talent, and I stand by it too," spits M.I.A. on 'Bring The Noize' over war drums, gunfire stutters and rave synths, before proceeding to devolve into nonsense rhymes for a couple of lines. It's a neat riposte to the idea that, just when she seemed poised to take over the world, her bubble burst. A Grammy performance, nine months pregnant, alongside four kings of hip-hop - T.I., Jay-Z, Kanye West and Lil' Wayne - didn't turn her into a force in rap; a Superbowl appearance alongside Madonna and Nicki Minaj led only to faux-controversy and sour recriminations. But, as Matangi implies, perhaps M.I.A. is better off by herself. In both recent live performances and the official video of 'YALA', she performs on her own: no dancers, no DJs, just one woman, centre stage. It's a powerful statement: in a world where collaborations, allegiances and positioning hold increasing sway, M.I.A. is the ultimate lone wolf.