diff --git a/src/Matrix.jl b/src/Matrix.jl
index b52390798..08f4eb49e 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -3700,8 +3700,9 @@ such that $A^k = 0$. If `A` is not square an exception is raised.
 """
 function is_nilpotent(A::MatrixElem{T}) where {T <: RingElement}
   !is_square(A) && error("Dimensions don't match in is_nilpotent")
-  A = deepcopy(A)
+  is_zero(tr(A)) || return false
   n = nrows(A)
+  A = deepcopy(A)
   i = 1
   is_zero(A) && return true
   while i < n
diff --git a/test/Matrix-test.jl b/test/Matrix-test.jl
index 5f5776699..dd206c611 100644
--- a/test/Matrix-test.jl
+++ b/test/Matrix-test.jl
@@ -66,8 +66,9 @@ end
 
 @testset "Matrix.is_nilpotent" begin
   @test is_nilpotent(zero_matrix(QQ, 3, 3))
-  @test !is_nilpotent(identity_matrix(QQ, 3))
   @test is_nilpotent(upper_triangular_matrix(QQ.([0,1,1,0,1,0])))
+  @test !is_nilpotent(identity_matrix(QQ, 3))
+  @test !is_nilpotent(diagonal_matrix(QQ, [1,-1,0]))
 end
 
 @testset "Matrix.concat" begin