diff --git a/src/tracker/lib/array.jl b/src/tracker/lib/array.jl
index 023f5fa2..e8239aad 100644
--- a/src/tracker/lib/array.jl
+++ b/src/tracker/lib/array.jl
@@ -125,7 +125,7 @@ Base.adjoint(xs::TrackedArray) = track(adjoint, xs)
 @grad adjoint(xs) = data(xs)', Δ -> (trim(xs, Δ'),)
 
 det(xs::TrackedArray) = track(det, xs)
-@grad det(xs) = det(data(xs)), Δ -> (Δ * transpose(adjoint(xs)),)
+@grad det(xs) = det(data(xs)), Δ -> (Δ * det(xs) * transpose(inv(xs)),)
 
 Base.repeat(xs::TrackedArray; kw...) = track(repeat, xs; kw...)