diff --git a/Mathlib/Analysis/CStarAlgebra/Matrix.lean b/Mathlib/Analysis/CStarAlgebra/Matrix.lean
index c304aa4b11eae3..d947cbdf360114 100644
--- a/Mathlib/Analysis/CStarAlgebra/Matrix.lean
+++ b/Mathlib/Analysis/CStarAlgebra/Matrix.lean
@@ -5,6 +5,7 @@ Authors: Hans Parshall
 -/
 module
 
+public import Mathlib.Analysis.CStarAlgebra.Classes
 public import Mathlib.Analysis.InnerProductSpace.Adjoint
 public import Mathlib.Analysis.Matrix.Normed
 public import Mathlib.Analysis.RCLike.Basic
@@ -289,6 +290,12 @@ lemma instCStarRing : CStarRing (Matrix n n 𝕜) where
 
 scoped[Matrix.Norms.L2Operator] attribute [instance] Matrix.instCStarRing
 
+/-- The matrices Matrix n n ℂ with the L2 operator norm form a CStarAlgebra. -/
+@[instance_reducible] noncomputable def instCStarAlgebra {n : Type*} [Fintype n] [DecidableEq n] :
+    CStarAlgebra (Matrix n n ℂ) where
+
+scoped[Matrix.Norms.L2Operator] attribute [instance] Matrix.instCStarAlgebra
+
 end Matrix
 
 end L2OpNorm