diff --git a/geom.go b/geom.go
index 2f449ae20..f94d7081c 100644
--- a/geom.go
+++ b/geom.go
@@ -83,6 +83,18 @@ func (g *GeoM) Translate(tx, ty float64) {
 	g.impl = g.impl.Translate(tx, ty)
 }
 
+// IsInvertible returns a boolean value indicating
+// whether the matrix g is invertible or not.
+func (g *GeoM) IsInvertible() bool {
+	return g.impl.IsInvertible()
+}
+
+// Invert inverts the matrix.
+// If g is not invertible, Invert panics.
+func (g *GeoM) Invert() {
+	g.impl = g.impl.Invert()
+}
+
 // Rotate rotates the matrix by theta.
 // The unit is radian.
 func (g *GeoM) Rotate(theta float64) {
diff --git a/geom_test.go b/geom_test.go
index 11ac27938..8cecf03b9 100644
--- a/geom_test.go
+++ b/geom_test.go
@@ -15,6 +15,7 @@
 package ebiten_test
 
 import (
+	"fmt"
 	"math"
 	"testing"
 
@@ -116,6 +117,16 @@ func TestGeoMConcatSelf(t *testing.T) {
 	}
 }
 
+func geoMToString(g GeoM) string {
+	a := g.Element(0, 0)
+	b := g.Element(0, 1)
+	c := g.Element(1, 0)
+	d := g.Element(1, 1)
+	tx := g.Element(0, 2)
+	ty := g.Element(1, 2)
+	return fmt.Sprintf("{a: %f, b: %f, c: %f, d: %f, tx: %f, ty: %f}", a, b, c, d, tx, ty)
+}
+
 func TestGeoMApply(t *testing.T) {
 	trans := GeoM{}
 	trans.Translate(1, 2)
@@ -172,7 +183,91 @@ func TestGeoMApply(t *testing.T) {
 	for _, c := range cases {
 		rx, ry := c.GeoM.Apply(c.InX, c.InY)
 		if math.Abs(rx-c.OutX) > c.Delta || math.Abs(ry-c.OutY) > c.Delta {
-			t.Errorf("%v.Apply(%v, %v) = (%v, %v), want (%v, %v)", c.GeoM, c.InX, c.InY, rx, ry, c.OutX, c.OutY)
+			t.Errorf("%s.Apply(%f, %f) = (%f, %f), want (%f, %f)", geoMToString(c.GeoM), c.InX, c.InY, rx, ry, c.OutX, c.OutY)
+		}
+	}
+}
+
+func TestGeoMIsInvert(t *testing.T) {
+	zero := GeoM{}
+	zero.Scale(0, 0)
+
+	trans := GeoM{}
+	trans.Translate(1, 2)
+
+	scale := GeoM{}
+	scale.Scale(1.5, 2.5)
+
+	cpx := GeoM{}
+	cpx.Rotate(math.Pi)
+	cpx.Scale(1.5, 2.5)
+	cpx.Translate(-2, -3)
+
+	cases := []struct {
+		GeoM       GeoM
+		Invertible bool
+	}{
+		{
+			GeoM:       zero,
+			Invertible: false,
+		},
+		{
+			GeoM:       GeoM{},
+			Invertible: true,
+		},
+		{
+			GeoM:       trans,
+			Invertible: true,
+		},
+		{
+			GeoM:       scale,
+			Invertible: true,
+		},
+		{
+			GeoM:       cpx,
+			Invertible: true,
+		},
+	}
+
+	pts := []struct {
+		X float64
+		Y float64
+	}{
+		{
+			X: 0,
+			Y: 0,
+		},
+		{
+			X: 1,
+			Y: 1,
+		},
+		{
+			X: 3.14159,
+			Y: 2.81828,
+		},
+		{
+			X: -1000,
+			Y: 1000,
+		},
+	}
+
+	const delta = 0.00001
+
+	for _, c := range cases {
+		if c.GeoM.IsInvertible() != c.Invertible {
+			t.Errorf("%s.IsInvertible(): got: %t, want: %t", geoMToString(c.GeoM), c.GeoM.IsInvertible(), c.Invertible)
+		}
+		if !c.GeoM.IsInvertible() {
+			continue
+		}
+		invGeoM := c.GeoM
+		invGeoM.Invert()
+		for _, p := range pts {
+			x, y := p.X, p.Y
+			gotX, gotY := invGeoM.Apply(c.GeoM.Apply(x, y))
+			if math.Abs(gotX-x) > delta || math.Abs(gotY-y) > delta {
+				t.Errorf("%s.Apply(%s.Apply(%f, %f)): got: (%f, %f), want: (%f, %f)", geoMToString(invGeoM), geoMToString(c.GeoM), x, y, gotX, gotY, x, y)
+			}
 		}
 	}
 }
diff --git a/internal/affine/geom.go b/internal/affine/geom.go
index cfb947a34..6cb73f0d6 100644
--- a/internal/affine/geom.go
+++ b/internal/affine/geom.go
@@ -183,3 +183,32 @@ func (g *GeoM) Rotate(theta float64) *GeoM {
 		ty:  sin*g.tx + cos*g.ty,
 	}
 }
+
+func (g *GeoM) det() float64 {
+	if g == nil {
+		return 1
+	}
+	return (g.a_1+1)*(g.d_1+1) - g.b - g.c
+}
+
+func (g *GeoM) IsInvertible() bool {
+	return g.det() != 0
+}
+
+func (g *GeoM) Invert() *GeoM {
+	if g == nil {
+		return nil
+	}
+	det := g.det()
+	if det == 0 {
+		panic("affine: g is not invertible")
+	}
+	return &GeoM{
+		a_1: ((g.d_1 + 1) / det) - 1,
+		b:   -g.b / det,
+		c:   -g.c / det,
+		d_1: ((g.a_1 + 1) / det) - 1,
+		tx:  (-(g.d_1+1)*g.tx + g.b*g.ty) / det,
+		ty:  (g.c*g.tx + -(g.a_1+1)*g.ty) / det,
+	}
+}