diff --git a/tests/issues/run.bat b/tests/issues/run.bat
index dcea3d483..7ed43205d 100644
--- a/tests/issues/run.bat
+++ b/tests/issues/run.bat
@@ -16,6 +16,7 @@ set COMMON=-define:ODIN_TEST_FANCY=false -file -vet -strict-style
 ..\..\..\odin test ..\test_issue_2637.odin %COMMON%  || exit /b
 ..\..\..\odin test ..\test_issue_2666.odin %COMMON%  || exit /b
 ..\..\..\odin test ..\test_issue_4210.odin %COMMON%  || exit /b
+..\..\..\odin test ..\test_issue_4584.odin %COMMON%  || exit /b
 
 @echo off
 
diff --git a/tests/issues/run.sh b/tests/issues/run.sh
index c3bc00e24..54543980e 100755
--- a/tests/issues/run.sh
+++ b/tests/issues/run.sh
@@ -17,6 +17,7 @@ $ODIN test ../test_issue_2615.odin $COMMON
 $ODIN test ../test_issue_2637.odin $COMMON
 $ODIN test ../test_issue_2666.odin $COMMON
 $ODIN test ../test_issue_4210.odin $COMMON
+$ODIN test ../test_issue_4584.odin $COMMON
 if [[ $($ODIN build ../test_issue_2395.odin $COMMON 2>&1 >/dev/null | grep -c "Error:") -eq 2 ]] ; then
 	echo "SUCCESSFUL 1/1"
 else
diff --git a/tests/issues/test_issue_4584.odin b/tests/issues/test_issue_4584.odin
new file mode 100644
index 000000000..b80ecb3d9
--- /dev/null
+++ b/tests/issues/test_issue_4584.odin
@@ -0,0 +1,56 @@
+// Tests issue #4584 https://github.com/odin-lang/Odin/issues/4584
+package test_issues
+
+import "core:testing"
+import "core:math/linalg"
+
+@test
+test_adjugate_2x2 :: proc(t: ^testing.T) {
+	m := matrix[2,2]int {
+		-3, 2,
+		-1, 0,
+	}
+	expected := matrix[2,2]int {
+		 0, -2,
+		 1, -3,
+	}
+	testing.expect_value(t, linalg.adjugate(m), expected)
+	testing.expect_value(t, linalg.determinant(m), 2)
+	testing.expect_value(t, linalg.adjugate(m) * m, 2 * linalg.identity(matrix[2,2]int))
+}
+
+@test
+test_adjugate_3x3 :: proc(t: ^testing.T) {
+	m := matrix[3,3]int {
+		-3,  2, -5,
+		-1,  0, -2,
+		 3, -4,  1,
+	}
+	expected := matrix[3,3]int {
+		-8, 18, -4,
+		-5, 12, -1,
+		 4, -6,  2,
+	}
+	testing.expect_value(t, linalg.adjugate(m), expected)
+	testing.expect_value(t, linalg.determinant(m), -6)
+	testing.expect_value(t, linalg.adjugate(m) * m, -6 * linalg.identity(matrix[3,3]int))
+}
+
+@test
+test_adjugate_4x4 :: proc(t: ^testing.T) {
+	m := matrix[4,4]int {
+		-3,  2, -5, 1,
+		-1,  0, -2, 2,
+		 3, -4,  1, 3,
+		 4,  5,  6, 7,
+	}
+	expected := matrix[4,4]int {
+		-144,  266, -92, -16,
+		  57,   92,  -5, -16,
+		 105, -142,  55,   2,
+		  33,  -96,   9,  -6,
+	}
+	testing.expect_value(t, linalg.adjugate(m), expected)
+	testing.expect_value(t, linalg.determinant(m), -174)
+	testing.expect_value(t, linalg.adjugate(m) * m, -174 * linalg.identity(matrix[4,4]int))
+}
\ No newline at end of file