diff --git a/Project.toml b/Project.toml
index 29f0e2bc8..1b464db86 100644
--- a/Project.toml
+++ b/Project.toml
@@ -31,7 +31,7 @@ Aqua = "0.6, 0.7, 0.8"
 CUDA = "6"
 ChainRulesCore = "1"
 ChainRulesTestUtils = "1"
-Enzyme = "0.13.131"
+Enzyme = "0.13.148"
 EnzymeTestUtils = "0.2.5"
 GenericLinearAlgebra = "0.3.19, 0.4"
 GenericSchur = "0.5.6"
diff --git a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
index 57bc92a53..a7014a463 100644
--- a/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
+++ b/ext/MatrixAlgebraKitEnzymeExt/MatrixAlgebraKitEnzymeExt.jl
@@ -67,13 +67,13 @@ for (f, pb) in (
             # so we do not need to cache it. This may change if future pullbacks
             # depend directly on A!
             ret = func.val(A.val, arg.val, alg.val)
-            # if arg.val == ret, the annotation must be Duplicated or DuplicatedNoNeed
+            # if arg.val === ret, the annotation must be Duplicated or DuplicatedNoNeed
             # if arg isa Const, ret may still be modified further down the call graph so we should
             # copy it to protect ourselves
             A_is_arg1 = !isa(A, Const) && A.val === arg.val[1]
             A_is_arg2 = !isa(A, Const) && A.val === arg.val[2]
             A_is_arg = A_is_arg1 || A_is_arg2
-            cache_arg = (arg.val !== ret && !A_is_arg) || EnzymeRules.overwritten(config)[3] ? copy.(ret) : nothing
+            cache_arg = arg.val !== ret || A_is_arg || EnzymeRules.overwritten(config)[3] ? copy.(ret) : nothing
             dret = if EnzymeRules.needs_shadow(config) && ((TA == Nothing && TB == Nothing) || isa(arg, Const))
                 make_zero.(ret)
             elseif EnzymeRules.needs_shadow(config)