diff --git a/test/matrices/involutory.jl b/test/matrices/involutory.jl
new file mode 100644
index 0000000..6b1b8ee
--- /dev/null
+++ b/test/matrices/involutory.jl
@@ -0,0 +1,14 @@
+# constructors
+@test allequal([
+    Involutory(5),
+    Involutory{Int}(5),
+])
+
+# linear algebra functions
+run_test_linearalgrbra_functions(Involutory.(1:5))
+
+# eltype
+@test test_matrix_elements(Involutory{Int32}(5))
+
+# content
+@test Involutory(5) ≈ [-5.0 0.5 0.3333333333333333 0.25 0.2; -300.0 40.0 30.0 24.0 20.0; 1050.0 -157.5 -126.0 -105.0 -90.0; -1400.0 224.0 186.66666666666666 160.0 140.0; 630.0 -105.0 -90.0 -78.75 -70.0]