Winforms Drag & Drop image with transparency

I have the following code:

        private void button1_MouseDown(object sender, MouseEventArgs e)
        {
            Button btn = sender as Button;
            using (Bitmap bmp = new Bitmap(btn.Width, btn.Height))
            {
                btn.DrawToBitmap(bmp, new Rectangle(Point.Empty, btn.Size));
                using (Graphics gfx = Graphics.FromImage(bmp))
                {
                    ColorMatrix matrix = new ColorMatrix();
                    matrix.Matrix33 = .5F;
                    ImageAttributes attributes = new ImageAttributes();
                    attributes.SetColorMatrix(matrix, ColorMatrixFlag.Default, ColorAdjustType.Bitmap);
                    gfx.DrawImage(bmp, new Rectangle(Point.Empty, bmp.Size));
                    Cursor cur = new Cursor(bmp.GetHicon());
                    Cursor.Current = cur;
                }
            }
        }

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It's supposed to draw the image with transparency but it's opaque. How do I add alpha channel info? My ultimate goal is to have an alpha channel gradient so the transparency increases as the image gets further away from a given point (usually the center or the left edge).