add a Button (button1) and a Panel (panel1) on your main form.
FormA is that as you said.
add following code on button1.click event.
private void button1_Click(object sender, EventArgs e) {
FormA frm = new FormA();
frm.TopLevel = false;
frm.Parent = this.panel1;
frm.Dock = DockStyle.Fill;
frm.Show();
}
is this what you want?