diff --git a/src/pdsparsemat.jl b/src/pdsparsemat.jl
index c97fe9a..4036076 100644
--- a/src/pdsparsemat.jl
+++ b/src/pdsparsemat.jl
@@ -51,7 +51,7 @@ end
 
 ### Algebra
 
-Base.inv(a::PDSparseMat{T}) where {T<:Real} = PDMat( a\eye(T,a.dim) )
+Base.inv(a::PDSparseMat{T}) where {T<:Real} = PDMat(inv(a.mat))
 LinearAlgebra.logdet(a::PDSparseMat) = logdet(a.chol)
 
 ### whiten and unwhiten