Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single-scattering assumption. In heterogeneous areas such as volcanoes, the multiple-scattering contribution limits the imaging-depth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof of concept, the case of the Erebus volcano in Antarctica is considered. The Green's functions between a set of geophones placed on top of the volcano are first retrieved by the cross correlation of coda waves induced by multiple icequakes. This set of impulse responses forms a reflection matrix. By combining a matrix discrimination of singly scattered waves with iterative time reversal, we are able to push back the multiple scattering limit beyond 10 scattering mean free paths. The matrix approach reveals the internal structure of the Erebus volcano: A chimney-shaped structure at shallow depths, a magma reservoir at 2,500 m and several cavities at sea level and below it. The matrix approach paves the way toward a greatly improved monitoring of volcanic structures at depth. Beyond this specific case, the matrix approach of seismic imaging can generally be applied to all scales and areas where multiple scattering events undergone by body waves prevent in-depth imaging of the Earth's crust.